Derivatives. Immediate and basic operations

Derivatives

Multiple Choice

Calculate the derivative of  $$f\left(x\right)=781$$  

• $$f'\left(x\right)=0$$  

• $$f'\left(x\right)=1$$  

• $$f'\left(x\right)=781$$  

• $$f'\left(x\right)=781x$$  

• I don't know how to do this one

Constant function

Multiple Choice

Calculate the derivative of  $$f\left(x\right)=x^9$$  

• $$f'\left(x\right)=0$$  

• $$f'\left(x\right)=9$$  

• $$f'\left(x\right)=9x^9$$  

• $$f'\left(x\right)=9x^8$$  

• I don't know how to do this one

Function with real exponent

Multiple Choice

Calculate the derivative of  $$g\left(x\right)=2^x$$  

• $$g'\left(x\right)=x\cdot2^{x-1}$$  

• $$g'\left(x\right)=2^x$$  

• $$g'\left(x\right)=2^x\cdot\ln\left(2\right)$$  

• $$g'\left(x\right)=\frac{\ln\left(2\right)}{x}$$  

• I don't know how to do this one

Exponential function

Multiple Choice

Calculate the derivative of  $$h\left(x\right)=6\ln\left(x\right)$$  

• $$h'\left(x\right)=6\ln\left(x\right)$$  

• $$h'\left(x\right)=6e^x$$  

• $$h'\left(x\right)=\frac{1}{x}$$

• $$h'\left(x\right)=\frac{6}{x}$$  

• I don't know how to do this one

​Natural logarithm function

Multiple Choice

Calculate the derivative of  $$f\left(x\right)=7^x-7x^7$$  

• $$f'\left(x\right)=7^x+7x^6$$  

• $$f'\left(x\right)=7^x-49x^6$$  

• $$f'\left(x\right)=7^x·\ln7+7x^6$$

• $$f'\left(x\right)=7^x·\ln7-49x^6$$  

• I don't know how to do this one

Exponential and product function by real number

Multiple Choice

Calculate the derivative of  $$p\left(x\right)=\log_3\left(x\right)+6$$  

• $$p'\left(x\right)=\frac{\log_3\left(e\right)}{x}$$  

• $$p'\left(x\right)=\frac{\log_3\left(x\right)}{x}$$  

• $$p'\left(x\right)=\frac{\log_3\left(e\right)}{x}+6$$

• $$p'\left(x\right)=\frac{3}{x}$$  

• I don't know how to do this one

Logarithm and constant function

Multiple Choice

Calculate the derivative of  $$f\left(x\right)=30x^4$$  

• $$120x$$  

• $$12x^3$$  

• 0

• $$120x^3$$  

• $$12x$$  

First, since it is a product of a constant, we must keep the constant and differentiate the function.

Multiple Choice

Calculate the derivative of  $$f\left(x\right)=-x^2$$  

• $$2x$$  

• $$-2x$$  

• 0

• 2

​In this case, we must consider that since it is negative, it means that it is multiplied by (-1), therefore, it must be maintained.

Multiple Choice

Calculate the derivative of  $$f\left(x\right)=4-x^4$$  

• $$4x^3$$  

• $$4-4x^3$$  

• $$4+4x^3$$  

• $$-4x^3$$  

Multiple Choice

$$f\left(x\right)=\sqrt{x}+2x$$  

• $$f'\left(x\right)=\sqrt{x}$$  

• $$f'\left(x\right)=2$$  

• $$f'\left(x\right)=\frac{1}{2\sqrt{x}}+2$$  

• $$f'\left(x\right)=\sqrt{x}+2$$  

First, since it is a subtraction of functions, we must differentiate each of the functions separately and then subtract them.

Multiple Choice

Calculate the derivative of  $$h\left(x\right)=x\cdot\ln\left(x\right)$$  

• $$\frac{1}{x}$$  

• $$\ln\left(x\right)+x\cdot\frac{1}{x}$$  

• $$x\cdot\frac{1}{x}$$  

• $$1$$  

First, since it is a multiplication of functions, we must follow the following rule:

Multiple Choice

Calculate the derivative of  $$g\left(x\right)=\left(x^3-2\right)^4$$  

• $$4\left(x^3-2\right)^3$$  

• $$4x^3\cdot3x^2$$  

• $$4\left(3x^2\right)^3$$  

• $$4\left(x^3-2\right)^3\cdot3x^2$$

En este caso, tenemos una función compuesta, por lo que primero debemos derivar la función externa y luego multiplicar por la derivada de la función interna.

Multiple Choice

Calculate the derivative of  $$f\left(x\right)=4\cdot e^x$$  

• $$0$$  

• $$4$$  

• $$e^x$$  

• $$4\cdot e^x$$  

Since it is a product of a function by real number, we keep the constant and differentiate the function.

​In this case, since it is the exponential in base "e", it remains the same.

Multiple Choice

Calculate the derivative of  $$f\left(x\right)=e^{4x^2}$$  

• $$e^{4x^2}$$  

• $$4x$$  

• $$4x\cdot e^{4x^2}$$  

• $$4\cdot e^{4x^2}$$  

Multiple Choice

$$f\left(x\right)=50\ln3$$  

• $$f'\left(x\right)=0$$  

• $$f'\left(x\right)=50$$  

• $$f'\left(x\right)=\frac{50}{\ln3}$$  

• $$f'\left(x\right)=50\ ·\ \frac{1}{\ln3}$$

Multiple Choice

$$f\left(x\right)=\frac{x}{3}+\frac{e}{5}$$  

• $$f´\left(x\right)=\frac{1}{3}+\frac{e}{5}$$  

• $$f'\left(x\right)=\frac{8}{15}$$  

• $$f'\left(x\right)=\frac{1}{3}$$  

• $$f'\left(x\right)=\frac{e}{5}$$  

Multiple Choice

$$f\left(x\right)=150x$$  

• $$f'\left(x\right)=0$$  

• $$f'\left(x\right)=x$$  

• $$f'\left(x\right)=150$$  

• $$f'\left(x\right)=300x^2$$  

Multiple Choice

$$f\left(x\right)=7x+5\pi+50$$  

• $$f´\left(x\right)=7$$  

• $$f'\left(x\right)=57+5\pi$$  

• $$f'\left(x\right)=0$$  

• $$f'\left(x\right)=7x+5\pi$$  

Multiple Choice

$$f\left(x\right)=\frac{x^2}{2}+5$$  

• $$f'\left(x\right)=x$$  

• $$f'\left(x\right)=2x+5$$  

• $$f'\left(x\right)=2x+5$$  

• $$f'\left(x\right)=\frac{1}{2}$$  

Multiple Choice

$$f\left(x\right)=x^6$$  

• $$f'\left(x\right)=x^5$$  

• $$f'\left(x\right)=x^6$$  

• $$f'\left(x\right)=6x^5$$   

• $$f'\left(x\right)=6x$$  f'(x)=6x

Multiple Choice

$$f\left(x\right)=5x^2+10x$$  

• $$f'\left(x\right)=5x+10$$  

• $$f'\left(x\right)=10x$$  

• $$f'\left(x\right)=5$$  

• $$f'\left(x\right)=10x+10$$  

Multiple Choice

$$f\left(x\right)=\frac{1}{x}$$  

• $$f'\left(x\right)=0$$  

• $$f'\left(x\right)=\frac{1}{x^2}$$  

• $$f'\left(x\right)=-\frac{1}{x^2}$$  

Multiple Choice

$$f\left(x\right)=\ 2x^2+7x+2$$  

• $$f'\left(x\right)=2x+7$$  

• $$f'\left(x\right)=4x-7$$  

• $$f'\left(x\right)=4x+7$$  

Multiple Choice

$$f\left(x\right)=\frac{x^3}{4}+2x$$  

• $$f'\left(x\right)=\frac{1}{4}x^2$$  

• $$f'\left(x\right)=\frac{3}{4}x^2+2$$  

• $$f'\left(x\right)=\frac{3}{4}x^2$$  

Multiple Choice

$$f\left(x\right)=\sqrt{x}+2x$$  

• $$f'\left(x\right)=\sqrt{x}$$  

• $$f'\left(x\right)=2$$  

• $$f'\left(x\right)=\frac{1}{2\sqrt{x}}+2$$  

• $$f'\left(x\right)=\sqrt{x}+2$$  

Multiple Choice

$$f\left(x\right)=\frac{x^4}{2}+3x^2$$  

• $$f'\left(x\right)=2x^3+6x$$  

• $$f'\left(x\right)=\frac{x^3}{2}+3x$$  

• $$f'\left(x\right)=4x^3+3$$  

Multiple Choice

$$f\left(x\right)=\frac{6}{7}x+\frac{1}{x}$$  

• $$f'\left(x\right)=\frac{6}{7}-\frac{1}{x^2}$$  

• $$f'\left(x\right)=\frac{15}{7}$$  

• $$f'\left(x\right)=\frac{6}{7}x$$  

• $$f'\left(x\right)=\frac{1}{2}x^2$$  

Multiple Choice

Calculate the derivative of the following function: $$3x^2-5x\ +8$$  

• 6x-5

• $$6x^2+5$$  

• 6x+5

• 5x-5

Multiple Choice

Differenciate of the following function: $$8x^4-7x^3+15x^2-233x+43$$  

• $$32x^3-21x^2+30x-233$$  

• $$32x-21x^2+30x-233$$  

• $$32x^3+21x^2-30x+233$$  

• $$32x^4-21x^3+30x^2-233x+43$$  

Multiple Choice

Calculate the derivative of the following function: $$12x^{12}+10x^7$$  

• 12x+10x

• $$144x^{11}+70x^6$$  

• $$120x^{10}-70x^{13}$$  

• $$144x^{11}-70x^6$$  

Multiple Choice

If $$f\left(x\right)=e^{8x}+x^2-25$$   then its derivative is

• $$f'\left(x\right)=e^{8x}+2x$$  

• $$f´\left(x\right)=8e^{8x}+2x$$  

• $$f'\left(x\right)=8e^x+2$$  

• $$8e^{7x}+2x$$  

Multiple Choice

Calculate the derivative of the function:

y = 3x

• 0

• 3x²

• 3

• 6x

Multiple Choice

Calculate the derivative of the function:

f(x) = x⁷

• x⁶

• 7x⁶

• 7x⁸

• 7x⁷

Multiple Choice

The derivative of the function f(x)=5x³-4x² is

• -45x² +5

• 15x² - 8x

• -15x² +4x

• 15x-8x

Multiple Choice

f(x)=4x^-4+ 5x

• f´(x)= - 16x^-3 + 5

• f´(x)= -16x³ + 5

• f´(x)= 16x⁵ + 5

• f´(x) = -16x^-5 + 5

Multiple Choice

What is the derivative of x⁵?

• 5x⁶

• 5x⁵

• 5x⁴

• 5x

Multiple Choice

What is the derivative of x^-2?

• 2x^-1

• -2x^-3

• 2x^-3

• -2x³

Multiple Choice

What is the derivative of $$\frac{2}{3}x^3$$ ?

• 2 x²

• x²/3

• 2 x⁴

• x⁴/3

Multiple Choice

What is the derivative of x?

• 0

• 1

• x

• x²

Multiple Choice

What is the derivative of -8?

• -8

• 8

• 0

• 1

Multiple Choice

Differenciate the function $$f\left(x\right)=2x^{-4}+4x$$  

• $$\text{f' (x)}=8x^{-5}+4x$$  

• $$\text{f' (x)}=-8x^{-5}+4$$  

• $$\text{f'(x)}=-8x^{-4}+4$$  

• $$f'\ \left(x\right)=8x^{-4}+4x$$  

Multiple Choice

The derivative of a constant is...

• 1

• 0

• ∄

Multiple Choice

Differenciate the function $$f\left(x\right)=2x^2\left(x^3+3\right)$$  

• $$\text{f' (x)}=2x^5+6x^2$$  

• $$\text{f' (x)}=10x^6+6x$$  

• $$\text{f' (x)}=10x^4-12$$  

• $$\text{f' (x)}=10x^4+12x$$  

Multiple Choice

The derivative of the function $$f\left(x\right)=2x^2-1$$  is

• $$4x$$  

• $$4$$  

• $$4x^2$$  

• $$2x$$  

Multiple Choice

The derivative of the function $$f\left(x\right)=\ \frac{\left(x-1\right)}{x}$$  is...

• $$-1$$  

• $$\frac{\left(-x^2+2x\right)}{x^2}$$  

• $$\frac{1}{x^2}$$  

• $$-\frac{1}{x^2}$$  

Multiple Choice

The derivative of the function

$$f\left(x\right)=\ 2x^2+7x+2$$   is...

• $$f\left(x\right)´=2x+7$$  

• $$f\left(x\right)´=4x-7$$  

• $$f\left(x\right)´=4x+7$$  

Multiple Choice

The derivative of the function

$$f\left(x\right)=\frac{2}{5}x^3+5x^2+\pi$$  

is...

• $$f'\left(x\right)=\frac{6}{5}x^2+10x$$  

• $$f'\left(x\right)=\frac{6}{5}x^2+10x+\pi$$  

• $$f'\left(x\right)=\frac{6}{10}x^2+10x$$  

Multiple Choice

What is the derivative of the following function?

$$f\left(x\right)=\frac{2}{x^2}+3x-4$$  

• $$f'\left(x\right)=\frac{4}{x^3}+3x$$  

• $$f'\left(x\right)=-\frac{4}{x^3}+3$$  

• $$f'\left(x\right)=-\frac{4}{x^3}+3x-4$$  

Multiple Choice

What is the derivative of the following function?

$$f\left(x\right)=\sqrt{x^3}$$  

• $$f'\left(x\right)=\frac{3}{2}\sqrt{x}$$  

• $$f'\left(x\right)=\frac{2}{3}\sqrt{x}$$  

• $$f'\left(x\right)=\sqrt{x}$$  

Multiple Choice

The derivative of the following function

$$f\left(x\right)=\frac{3}{2x}+3x\ \ \ \ \ \ \ \ \ \ \ is\ \ \ \ \ \ \ \ \ \ \ f\left(x\right)'=-\frac{3}{2x^2}+3x$$  

• True

• False

Multiple Choice

What is the derivative of the following function?

$$f\left(x\right)=^3\sqrt{x^7}+9x^2-\frac{3}{x^3}$$  

• $$f'\left(x\right)=\frac{7}{3}^3\sqrt{x^4}+9x^2+\frac{3}{x^4}$$  

• $$f'\left(x\right)=\frac{7}{3}^3\sqrt{x^4}+18x+\frac{3}{x^4}$$  

• $$f'\left(x\right)=\frac{7}{3}^3\sqrt{x^4}+18x+\frac{9}{x^4}$$  

Multiple Choice

The derivative of the following function

$$f\left(x\right)=\ 3x+8\ \ \ \ \ \ \ \ is\ \ \ \ \ \ \ \ \ \ f\left(x\right)'\ =\ 3$$  

• True

• False

Multiple Choice

What is the derivative of the following function?  $$f\left(x\right)=\ 7x^5+\ 2\pi x^2-5x$$  

• $$f'\left(x\right)=\ 35x^4+\ 2\pi x-5$$  

• $$f'\left(x\right)=\ 35x^4+\ 4x-5$$  

• $$f'\left(x\right)=\ 35x^4+\ 4\pi x-5$$  

Multiple Choice

Differenciate the following function:
$$y=x^3-2x^2-6$$

• $$x^2-2x$$  

• $$3x^2-4x$$  

• $$3x^2-4x-6$$  

• $$3^{ }x^3-2x^2$$  

Multiple Choice

Differenciate the following function: $$y=x^4-7x^3+2x^2+5$$  

• $$4x^3-21x^2+4x$$  

• $$x^3-7x^2+2x$$  

• $$4x^4-21x^3+4x^2$$  

• $$4x^4-21x^3+4x^2+5$$  

Multiple Choice

Differenciate the following function:

$$y=7x^4-2x^3+8x+5$$

• $$28x^4-6x^3+8x$$  

• $$28x^3-6x^2+8x$$  

• $$28x^3-6x^2+8$$  

• $$28x^3-6x^2$$  

Multiple Choice

Differenciate $$y=\frac{5x}{3}$$  

• $$\frac{5}{9}x$$  

• 5

• $$\frac{5}{3}$$  

• 0

Multiple Choice

Differenciate $$-\frac{3}{2}x$$  

• 0

• -3

• $$-\frac{3}{4}$$  

• $$-\frac{3}{2}$$  

Multiple Choice

Differenciate $$y=x-\frac{5}{7}$$

• $$-\frac{5}{7}$$  

• 0

• 1

• $$\frac{2}{7}$$  

Multiple Choice

Differenciate $$y=\frac{x}{5}+3$$

• $$\frac{1}{5}$$  

• 0

• 1

• 3

Multiple Choice

Differenciate $$y=\sqrt{7}\ +\ 2x$$

• 1

• $$\sqrt{7}$$  

• 2

• $$\frac{\sqrt{7}}{2}+2$$  

Multiple Choice

Differenciate $$y=x^3-2$$

• $$x^2$$  

• $$3x^2$$  

• $$3x^2-1$$  

• $$3x^3$$  

Multiple Choice

Differenciate $$y=\frac{\sqrt{5}}{3^{\frac{1}{3}}}-5x$$  

• $$\sqrt{5}-5$$  

• $$\frac{\sqrt{5}}{3^{\frac{1}{3}}}-5$$  

• 0

• -5

Multiple Choice

Differenciate $$y=\sqrt{7}+2$$  

• $$\sqrt{7}$$  

• 0

• 2

• 3

Multiple Choice

Differenciate $$y=x^{\frac{1}{3}}+x^3$$  

• $$\frac{1}{3}x^{-\frac{2}{3}}+3x^2$$  

• $$\frac{1}{3}x^{\frac{2}{3}}+3x^2$$  

• $$x^{\frac{2}{3}}+x^2$$  

• 1

Multiple Choice

Differenciate $$y=x^{-\frac{1}{2}}$$  

• $$-\frac{1}{2}x^{\frac{1}{2}}$$  

• $$-\frac{1}{2}x^{-\frac{1}{2}}$$  

• $$-\frac{1}{2}x^{-\frac{3}{2}}$$  

• $$x^{\frac{3}{2}}$$  

Multiple Choice

Differenciate $$y=\frac{5}{9}x+\frac{2}{9}$$  

• 0

• 1

• $$\frac{5}{9}$$  

• $$\frac{7}{9}$$  

Multiple Choice

Differenciate $$y=7-2x+4x^3-5x^4+8x^5-11x^2$$  

• $$-2+4x^2-5x^3+8x^4-11x$$  

• $$-2+12x^2-20x^3+40x^4-22x$$  

• $$-2+12x^3-20x^4+40x^5-22x^2$$  

• $$-1+6x^2-10x^3+20x^4-11x$$  

Multiple Choice

Differenciate $$y=x^{-1}+x^{-2}$$  

• $$x^{-2}+2x^{-3}$$  

• $$-x^2-2x^3$$  

• $$x^2+2x^3$$  

• $$-x^{-2}-2x^{-3}$$  

Multiple Choice

Differenciate   $$y=-3x^{-3}\ +\ 3x^{-4}$$  

• $$-9x^4-12x^5$$  

• $$9x^4+12x^5$$  

• $$9x^{-4}-12x^{-5}$$  

• $$-9x^{-4}-12x^{-5}$$