3.2 DIFFERENTIATION OF LOGARITHMIC FUNCTION

Differentiate

 $y=\frac{1}{3}\ln x$  

• 3/x

• 1/x

• x/3

• 1/3x

Differentiate y = ln (5x - 7)

• _ 5 _

  5x-7

• _ 1 _

  5x-7

• ln5

• ln5x - ln 7

Find  $\frac{dy}{dx}$  for  $y=\ln\left(\frac{2x+1}{1-2x}\right)$  .

•  $\frac{2}{2x+1}-\frac{2}{1-2x}$  

•  $\frac{2}{2x+1}+\frac{2}{1-2x}$  

•  $\frac{2}{2x-1}+\frac{2}{1-2x}$  

•  $\frac{2}{2x+1}+\frac{2}{1+2x}$  

 $g\left(x\right)=\ln\left(2x^3+1\right)$  

•  $-\frac{6x^2}{2x^3+1}$  

•  $\frac{6x^2}{2x^3+1}$  

•  $-\frac{1}{2x^3+1}$  

•  $\frac{1}{2x^3+1}$  

Find the differentiation of  $\ln\left(x^2+2\right)$  

•  $\frac{2}{x^2+2}$  

•  $\frac{2x}{x^2+2}$  

•  $2x$  

Find the differentiation of  $\ln\left(\sqrt{x^3+2x}\right)$  

•  $\frac{3x^2+2}{x^3+2x}$  

•  $\left(\frac{1}{2}.\frac{3x^2+2}{x^3+2x}\right)$  

•  $\frac{3x^2+2}{x^3+2}$  

Find the differentiation of  $\ln\left(x\sqrt{x}\right)$  

•  $\frac{3}{\sqrt{x}}$  

•  $\frac{x}{\sqrt{x}}$  

•  $\frac{3}{2x}$  

Find the differentiation of  $\ln\left(\frac{x}{x^2+5}\right)$  

•  $\ln x-\ln\left(x^2+5\right)$  

•  $\frac{1}{x}-\frac{2}{x^2+5}$  

•  $\frac{1}{x}-\frac{2x}{x^2+5}$