Logarithmic Differentiation

Logarithmic Differentiation

Examples

 $f\left(x\right)=e^{2x}\left(x+1\right)^3$  

 $f'\left(x\right)=?$  

Fill in the Blank

 $f\left(x\right)=e^{2x}\left(x+1\right)^3$  
 $Applying\ Ln\ :$  
 $\ln f\left(x\right)=$  

Fill in the Blank

 $f\left(x\right)=e^{2x}\left(x+1\right)^{3\ \ \ \ \ \ Then\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\frac{f'\left(x\right)}{f\left(x\right)}=$  

Multiple Choice

Solving by f'(x)=

• $f'\left(x\right)=\left(2+\frac{3}{\left(x+1\right)}\right)\left|fx\right|$

• $f"\left(x\right)=\ln\ \left(2x+\frac{3}{x+1}\right)e^{2x\ }\left(x+1\right)^3$

Multiple Choice

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)

Multiple Choice

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

•  $\frac{3x^2+2}{x^3+2x}$  

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

•  $\frac{3x^2+2}{x^3+2}$  

Multiple Choice

• a

• b

• c

• d

• e