Differentiate logarithms

What is the derivative of

 $y=\ln2x$  

•  $\frac{dy}{dx}=\frac{1}{2x}$  

•  $\frac{dy}{dx}=\frac{1}{x}$  

•  $\frac{dy}{dx}=\frac{2}{x}$  

•  $\frac{dy}{dx}=\frac{1}{x^2}$  

What is the derivative of

 $y=2\ln\left(x^2+3x\right)$  

•  $\frac{dy}{dx}=\frac{2x}{x^2+3x}$  

•  $\frac{dy}{dx}=\frac{2}{x^2+3x}$  

•  $\frac{dy}{dx}=\frac{2x+3}{x^2+3x}$  

•  $\frac{dy}{dx}=\frac{4x+6}{x^2+3x}$  

What is the derivative of

 $y=\ln\left(\frac{x}{2x+1}\right)$  

•  $\frac{dy}{dx}=\frac{1}{x}-\frac{2}{2x+1}$  

•  $\frac{dy}{dx}=\frac{1}{x}-\frac{1}{2x+1}$  

•  $\frac{dy}{dx}=\frac{1}{x}+\frac{2}{2x+1}$  

•  $\frac{dy}{dx}=\frac{1}{x}+\frac{1}{2x+1}$  

What is the derivative of

 $y=\ln\left(xe^x\right)$  

•  $\frac{dy}{dx}=\frac{1}{x}+e^x$  

•  $\frac{dy}{dx}=\frac{1}{x}+1$  

•  $\frac{dy}{dx}=\frac{1}{xe^x}$  

•  $\frac{dy}{dx}=\frac{1}{x}-1$  

What is the derivative of

 $y=\ln\left(x^2e^{x^2}\right)$  

•  $\frac{dy}{dx}=\frac{1}{2x}+e^{x^2}$  

•  $\frac{dy}{dx}=\frac{1}{2x}+2x$  

•  $\frac{dy}{dx}=\frac{2}{x}+2x$  

•  $\frac{dy}{dx}=\frac{1}{x^2}+2x$  

What is the derivative of

 $y=\ln\left(x^2+3\right)^5$ 

•  $\frac{dy}{dx}=\frac{10x}{x^2+3}$ 

•  $\frac{dy}{dx}=\frac{5x}{x^2+3}$ 

•  $\frac{dy}{dx}=\frac{2x}{x^2+3}$ 

•  $\frac{dy}{dx}=\frac{10}{x^2+3}$ 

What is the derivative of

 $y=\ln x^6$  

•  $\frac{dy}{dx}=\frac{1}{6x}$  

•  $\frac{dy}{dx}=\frac{6}{x}$  

•  $\frac{dy}{dx}=\frac{1}{6x}$  

•  $\frac{dy}{dx}=\frac{1}{x^6}$  

What is the derivative of

 $y=\ln\left(\frac{5x}{e^x}\right)$  

•  $\frac{dy}{dx}=\frac{1}{x}-1$  

•  $\frac{dy}{dx}=\frac{1}{x}+1$  

•  $\frac{dy}{dx}=\frac{1}{x}-e^x$  

•  $\frac{dy}{dx}=\frac{1}{x}+e^x$  

What is the derivative of

 $y=\ln\left(\frac{x^2+3}{x^3}\right)$  

•  $\frac{dy}{dx}=\frac{x}{x^2+3}-\frac{3}{x}$  

•  $\frac{dy}{dx}=\frac{2x}{x^2+3}-\frac{3}{x}$  

•  $\frac{dy}{dx}=\frac{1}{x^2+3}-\frac{1}{x^3}$  

•  $\frac{dy}{dx}=\frac{x}{x^2+3}-\frac{1}{x^3}$  

What is the derivative of

 $y=\ln\left(x\left(x^3+4\right)^5\right)$ 

•  $\frac{dy}{dx}=\frac{1}{x}+\frac{15x^2}{x^3+4}$ 

•  $\frac{dy}{dx}=\frac{1}{x}+\frac{3x^2}{x^3+4}$ 

•  $\frac{dy}{dx}=\frac{5}{x}+\frac{3x^2}{x^3+4}$ 

•  $\frac{dy}{dx}=\frac{5}{x}+\frac{5}{x^3+4}$