Question

# If $$\displaystyle y= \frac {\sqrt[3]{1+3x}\sqrt[4]{1+4x}\sqrt[5]{1+5x}}{\sqrt[7]{1+7x}\sqrt[8]{1+8x}}$$, then $$y'(0)$$ is equal to

A
1
B
1
C
2
D
Non existant

Solution

## The correct option is B $$1$$$$\displaystyle y= \frac {\sqrt[3]{1+3x}\sqrt[4]{1+4x}\sqrt[5]{1+5x}}{\sqrt[7]{1+7x}\sqrt[8]{1+8x}}$$Take log both sides,$$\displaystyle \log y = \frac{1}{3}\log(1+3x)+\frac{1}{4}\log(1+4x)+\frac{1}{5}\log(1+5x)-\frac{1}{7}\log(1+7x)-\frac{1}{8}\log(1+8x)$$ Differentiating both side w.r.t $$x$$$$\displaystyle \frac {1}{y}\times \frac {dy}{dx}=\frac {1}{(1+3x)}+\frac {1}{1+4x}+\frac {1}{1+5x}-\frac {1}{1+7x}-\frac {1}{1+8x}$$at $$x=0, y=1$$,  $$\therefore \displaystyle \frac {dy}{dx}=1+1+1-1-1=1$$Mathematics

Suggest Corrections

0

Similar questions
View More

People also searched for
View More