Derivative of Exponential and Logarithmic Functions

Find dy/dx for
y = 3^2x+5 

• dy/dx = 3^(2x+4)
• dy/dx = (3^(2x+4)) ln 3
• dy/dx = 3^(2x+5) ln3
• dy/dx = (3^(2x+5)) (ln 3) (2)

Differentiate:
f(x) = x³e^4x
*You will need to remove the Greatest Common Factor

• f '(x) = 3x²e^4x
• f '(x) = 3x²e^4x+3x²e^4x
• f '(x) = x²e^4x(4x+3)
• f '(x) = xe^4x(4x²+3x)

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:
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:
y=11^x²

• y′=11^x²(2x)(ln11)
• y′=2x(ln11)
• y′=11^x²(2x)(lnx)
• y′=11^x²(x)(ln11)

Find the second derivative of f(x) = x² + e^x  - cosx

• f"(x) = 2 + e^x + cosx
• f"(x) = 2x + e^x + cosx
• f"(x) = 2x + xe^x - cosx
• f"(x) = 2x + e^x + sinx

Find dy/dx

• A

• B

• C

• D

• 1/(3x²+5)^1/4
• (3x)/(2(3x²+5))
• (2(3x²+5)^3/4)/(3x)
• (3x²+5)^1/4

• (5(1-4x))/(12x³)
• 5(x+1)(3x³-4x²+4x-4)
• (5(x³+16))/(x(x³+4))
• (5(x+1)(-3x³+4x²-4x+4))/(3x⁴(x³+4))

Tags

CCSS.HSA.APR.D.6

• ((3x²-5)(x²+1))/(10x²(3x⁴-5))
• (2(-3x⁴-5))/(5x(3x⁴-5))
• (3x²-1)/(60x³)
• ((3x²-5)(-x²-1))/5

Tags

CCSS.HSA.APR.D.6