Natural Log and Exponential Derivatives

Find the derivative of  $y=\ln3x$  

•  $\frac{1}{x}$  

•  $\frac{1}{3x}$  

•  $\ln3\ +\ \ln x$  

•  $\frac{1}{\ln3x}$  

Derive y=e^3x

• e^3x

• 3e^3x

• 3x

• 3xe^3x

Find the derivative of  $y=\ln\left(x^2\right)$  

•  $\frac{1}{x^2}$  

•  $\frac{1}{x}$  

•  $\frac{2}{x}$  

•  $2\ln\left(x\right)$  

Find the derivative:

y=e^{4x^2-5x+6}

• e^{4x^2-5x+6}

• e^8x-5

• (8x-5)e^{4x^2-5x+6}

• (4x^2-5x+6)e^{4x^2-5x+6}

Find the derivative of  $y=\left(\ln x\right)^2$  

•  $\frac{1}{x^2}$  

•  $2\ln\left(x\right)$  

•  $\frac{2}{x}$  

•  $\frac{2\ln\left(x\right)}{x}$  

 $\frac{d}{dx}\left(4-e^{-5x}\right)^3$  

•  $3e^{-5x}\left(4-e^{-5x}\right)^2$  

•  $-15e^{-5x}\left(4-e^{-5x}\right)^2$  

•  $15e^{-5x}\left(4-e^{-5x}\right)^3$  

•  $e^{-5x}\left(4-e^{-5x}\right)^2$  

Find the derivative of  $y=x^2\ln3x$  

•  $\frac{2}{3}$  

•  $2$  

•  $2x\ln\left(3x\right)+\frac{x}{3}$  

•  $2x\ln\left(3x\right)+x$  

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)

• 1/(3x²+5)^1/4

• (3x)/(2(3x²+5))

• (2(3x²+5)^3/4)/(3x)

• (3x²+5)^1/4

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) = (2x-x²)/e^x

• D. f'(x) = x²e^x + 2xe^x