Derivatives Test

If f(x) = sec(4x), then f'(x) =

• 4sec(4x)tan(4x)
• 2sec(4x)tan(4x)
• -4csc(4x)cot(4x)
• -2csc(4x)cot(4x)

If f(x) = 4tan(x/2), then f'(x) =

• 4sec²(x/2)

• -4csc²(x/2)

• 2sec²(x/2)

• -2csc²(x/2)

Tags

CCSS.HSF.TF.C.8

If f(x) = -csc(x/2), then f'(x) = 

• sec²(x/2)
• 2csc(x/2)tan(x/2)
• ½csc(x/2)tan(x/2)
• -csc²(x/2)

Tags

CCSS.HSF.TF.C.9

If f(x) = sin³(2x), then f'(x) =

• 3cos(2x)
• 3sin(2x)⋅2
• 3sin²(2x)cos(2x)
• 3sin²(2x)cos(2x)⋅2

Tags

CCSS.HSF.TF.C.9

Derive y=e^3x

• y'=e^3x

• y'=3e^3x

• y'=3x

• y'=3xe^3x

Find the derivative f(x) = xe^x

• f'(x) = e^x

• f'(x) = xe^x + xe^x

• f'(x) = e^x - xe^x

• f'(x) = e^x + xe^x

Find the derivative:
y=4e^x²

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

Tags

CCSS.HSF-IF.C.8B

Find the derivative:

y=4e^3x²-4

• y'=4e^3x²-4

• y'=12xe^3x²-4

• y'=4xe^3x²-4

• y'=24xe^3x²-4

Find the derivative of  $f\left(x\right)=e^{5x^{5\ }}$  

•  $f'\left(x\right)=25x^4$  

•  $f'\left(x\right)=25x^4e^{5x^{5\ }}$  

•  $f'\left(x\right)=25x^4e^{5x^5-1}$  

•  $f'\left(x\right)=e^{5x^5}$  

Find the derivative:

y=5x²e^3x

(Remember to factor your answer)

• y'=10xe^3x(2x + 3)

• y'=5xe^3x(2 + 3x)

• y'=10ex^3x(3x + 2)

• y'=5xe^3x(2x + 3)