Derivatives of Exponential and Logarithmic Functions

What is the derivative of e^x?

• xe^x-1
• x^e
• e^x
• e^x-1

 $y=e^{4x}?$  Find the derivative of

•  $e^{4x}$  

•  $\frac{e^{4x}}{4}$  

•  $4e^{4x}$  

•  $-4e^{4x}$  

Tags

CCSS.HSF-IF.C.8B

Find the derivative:

y = 4e^x²

• y' = 8xe^x

• y' = 8xe^x²

• y' = 8xe^2x

• y' = 8xe^4x²

Tags

CCSS.HSF-IF.C.8B

The exact value of $f'\left(-2\right)$  if  $f\left(x\right)=2e^{-3x}$  is:

•  $-6e^6$  

•  $6e^6$  

•  $-6e^{-6}$  

•  $6e^{-6}$  

•  $-e^6$  

Tags

CCSS.HSF-IF.C.8B

If  $y=e^{-2x^3}$  , then  $\frac{\text{d}y}{\text{d}x}=$  

•  $-2x^3e^{-2x^3}$  

•  $e^{-2x^3}$  

•  $-6x^2e^{-2x^3}$  

•  $e^{-6x^2}$  

•  $-6x^2e^{-6x^2}$  

Find the derivative f(x) = xe^x

(Hint: Use product rule)

• f'(x) = e^x

• f'(x) = xe^x + xe^x

• f'(x) = e^x - xe^x

• f'(x) = e^x + xe^x

Differentiate $f\left(x\right)\ =2xe^{mx}$  

•  $2xe^{mx}+2me^{mx}$  

•  $2\left(e^{mx}+mxe^{mx}\right)$  

•  $2mxe^{mx}$  

•  $2e^{mx}+mxe^{mx}$  

Differentiating  $f\left(x\right)=\frac{\left(e^{2x}-e^x\right)^2}{e^x}$  yields:

(Hint: Expand and simplify $f\left(x\right)$  first, then differentiate)

•  $f'\left(x\right)=3e^{3x}+e^x$  

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

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

•  $f'\left(x\right)=e^{3x}+e^x$  

•  $\frac{1}{3}e^{3x}-e^{2x}+e^x$  

What is the derivative of ln(x)?

• xln(x)

• $\frac{1}{x}$

• $e^x$
  

• ln(x+1)

Differentiating  $-\ln\left(2x-3\right)$  yields:

•  $\frac{2}{2x-3}$  

•  $\frac{-1}{2x-3}$  

•  $\frac{1}{2x-3}$  

•  $-\frac{2}{2x-3}$  

•  $\frac{-3}{2x-3}$