Derivatives of the Natural Exponential Function

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

•  $A.\ \ \ \ -2x^3e^{-2x^3}$  

•  $B.\ \ \ \ \ \ e^{-2x^3}$  

•  $C.\ \ \ \ -6x^2e^{-2x^3}$  

•  $D.\ \ \ \ \ \ e^{-6x^2}$  

•  $E.\ \ \ \ \ -6x^2e^{-6x^2}$  

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

•  $A.\ \ \ \ \ -6e^6$  

•  $B.\ \ \ \ \ 6e^6$  

•  $C.\ \ \ \ -6e^{-6}$  

•  $D.\ \ \ \ \ 6e^{-6}$  

•  $E.\ \ \ \ \ -e^6$  

Tags

CCSS.HSF-IF.C.8B

What is the derivative of e^x?

• xe^x-1
• x^e
• e^x
• e^x-1

Derive y=e^3x

• e^3x
• 3e^3x
• 3x
• 3xe^3x

Tags

CCSS.HSF-IF.C.8B

Find the derivative f(x) = xe^x

• A. f'(x) = e^x

• B. f'(x) = xe^x + xe^x

• C. f'(x) = e^x - xe^x

• D. f'(x) = e^x + xe^x

Find the derivative.
f(x) = -8x^-3 + 5x - e^x

• f'(x) = -24x^-4 + 5 - e^x
• f'(x) = 24x^-4 + 5 - e^x
• f'(x) = 24x^-2 + 5 - e^x
• f'(x) = 24x^-4 + 5 - e^x-1

Tags

CCSS.7.EE.A.1

Find the derivative f(x) = x²/e^x

• A. f'(x) = (x²e^x - 2xe^x) / (e^x)²

• B. f'(x) = (2xe^x + x²e^x) / (e^x)²

• C. f'(x) = (2xe^x - x²e^x) / (e^x)²

• D. f'(x) = x²e^x + 2xe^x

Find the derivative:

y=4e^x²

• A. y'=8xe^x

• B. y'=8xe^x²

• C. y'=8xe^2x

• D. y'=8xe^4x²

Differentiate $y=√(e^{2x}+x)$  
##It is a combination of Chain Rule and Exponential function

•  $\frac{1}{2}\left(e^{2x}+x\right)^{-\frac{1}{2}}\times\left(e^{2x}+x\right)$  

•  $\frac{1}{2e^{2x}+1}$  

•  $\frac{2e^{2x}+1}{2\sqrt{e^{2x}+x}}$