Derivative Rules

Derivative Rules

Multiple Choice

What is the derivative of y=4

• 1

• 4

• 0

Multiple Choice

Find the derivative of:

 $f\left(x\right)=4\sqrt{x}$  

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

•  $f'\left(x\right)=2\sqrt{x}$  

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

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

Multiple Choice

Find the derivative of:

 $f\left(x\right)=x^9-7x^5+3x+13$  

•  $f'\left(x\right)=9x^8-35x^4+3$  

•  $f'\left(x\right)=x^8-7x^4+3$  

•  $f'\left(x\right)=9x^9-35x^5+3x$  

•  $f'\left(x\right)=9x^8-35x^4+3+13$  

Multiple Choice

 $\frac{d}{dx}\left[\ln x\right]=$  

•  $e^x$  
  

•  $\frac{1}{x}$  
  

•  $\frac{1}{\ln x}$  
  

•  $\frac{1}{e^x}$  
  

Multiple Choice

 $\frac{d}{dx}\left[e^x\right]=$  

•  $xe^{\left(x-1\right)}$  

•  $e^x$  

•  $xe^x\left(x-1\right)$  
  

•  $\ln x$  

Multiple Choice

Derivative of tanx

• cosx

• sinx

• secx

• sec²x

Multiple Choice

What is the derivative of cos(x)?

• sin(x)
• cos(x)
• -sin(x)
• -cos(x)

Multiple Choice

What is the derivative of y = 2π?

• 0

• 2

• -2

• None of the above

Multiple Choice

Let f(x) = (x - 1)(x + 2). Find f'(0)

• 0

• 1

• 2

• 3

Multiple Choice

Use the product rule to find the derivative. $f\left(x\right)\ =\ -x^3\left(3x^4-2\right)$  

•  $-3x^2+12x^3$  

•  $-21x^3+6x$  

•  $-21x^6+6x^2$  

•  $-84x^6-6x^2$  

Multiple Choice

Which option is using correctly the quotient rule?