Question

State True/False

If $y=sin\left(lo{g}_{e}x\right),$ then $\frac{dy}{dx}=\frac{\sqrt{1-y^2}}{x}$.

• A. True
• B. False

Answer 1

The correct option is A True

$y=sin\left(logx\right)$

Squaring both sides

$y^2=si{n}^2\left(logx\right)=1-co{s}^2\left(logx\right)$

So, $cos\left(logx\right)=\sqrt{1-y^2}$...........[1]

$y=sin\left(logx\right)$

Differentiate with respect to $x$

$\frac{dy}{dx}=\frac{cos\left(logx\right)}{x}=\frac{\sqrt{1-y^2}}{x}$........[from 1]