Logarithms and Exponential Derivative

Find the derivative of the function with respect to x:

 $y=e^{x^3-5x+1}$  

•  $\frac{dy}{dx}=e^{x^3-5x+1}\left(3x^2-5\right)$  

•  $\frac{dy}{dx}=3x^2e^{x^3-5x+1}$  

•  $\frac{dy}{dx}=e^{x^3-5x+1}\left(x^3-5x+1\right)$  

•  $\frac{dy}{dx}=3x^2-5$  

Find the derivative of the function with respect to x:

 $y=\ln\left(5x^4\right)$  

•  $\frac{dy}{dx}=\frac{4}{x}$  

•  $\frac{dy}{dx}=20x^3$  

•  $\frac{dy}{dx}=\frac{1}{5x^4}$  

•  $\frac{dy}{dx}=20x^3$  

Find the derivative of the function with respect to x:

 $y=\ln\left(\sin x\right)$  

•  $\frac{dy}{dx}=\frac{1}{\sin x}$  

•  $\frac{dy}{dx}=\cot x$  

•  $\frac{dy}{dx}=\tan x$  

•  $\frac{dy}{dx}=\frac{1}{\cos x}$  

Find the derivative of the function with respect to x:

 $y=\log_4x$  

•  $\frac{dy}{dx}=\frac{x}{\ln4}$  

•  $\frac{dy}{dx}=x\ln4$  

•  $\frac{dy}{dx}=\frac{\ln4}{x}$  

•  $\frac{dy}{dx}=\frac{1}{x\ln4}$  

Find the derivative of the function with respect to x:

 $y=\log\left(3x^2\right)$  

•  $\frac{dy}{dx}=\frac{6x}{\ln10}$  

•  $\frac{dy}{dx}=6x\ln10$  

•  $\frac{dy}{dx}=\frac{\ln10}{6x}$  

•  $\frac{dy}{dx}=\frac{1}{6x\ln10}$  

Find the derivative of the function with respect to x:

 $y=3^x$  

•  $\frac{dy}{dx}=3^x\ln3$  

•  $\frac{dy}{dx}=3^{x\ln3}$  

•  $\frac{dy}{dx}=\frac{3^x}{\ln3}$  

•  $\frac{dy}{dx}=\ln3^x$  

Find the derivative of the function with respect to x:

 $y=9^{x^2-8}$  

•  $\frac{dy}{dx}=9^{x^2-8}$  

•  $\frac{dy}{dx}=9^{x^2-8}\times\ln9$  

•  $\frac{dy}{dx}=9^{x^2-8}\times2x$  

•  $\frac{dy}{dx}=9^{x^2-8}\times\ln9\times2x$