Derivatives and Integrals of Exponential Functions of base e

If f(4) = 8 then f ^-1(8)=

(a)  

Tags

CCSS.HSF-BF.B.4C

If f(3) = 8, and f ' (3) = 7, then the derivative of the inverse of f(x) at x =8 is:

(a)  

Tags

CCSS.HSF-BF.B.4A

 $f\left(x\right)=x^3+3x$  
What is  $f\ '\ \left(2\right)?$  

• 14

• 15

• 0

• -1

Tags

CCSS.HSF.IF.A.2

Find the derivative:
y=4e^x²

• y'=8xe
• y'=8xe^x²
• y'=8xe^2x
• y'=8xe^4x²

Tags

CCSS.HSF-IF.C.8B

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:
y=e^5x

• y'=e^5x
• y'=5e^5x
• y'=5e^x
• y'=(1/5)e^5x

Tags

CCSS.HSF-IF.C.8B

Find the derivative:
y=5x²e^3x

• y'=10xe^3x(2x+3)
• y'=5xe^3x(3x+2)
• y'=10ex^3x(3x+2)
• y'=5xe^3x(2x+3)

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 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

What is the slope of the tangent line at $x=2$  if  $f\left(x\right)=2e^{-3x}$  ?

•  $-6e^6$  

•  $6e^6$  

•  $-6e^{-6}$  

•  $6e^{-6}$  

•  $-e^6$