Basic Derivative Rules

Derivative Rules

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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?