Question

If $y=\mathrm{loglog}x$, then $e^y\frac{dy}{dx}=$

• A. $\frac{1}{x}$
• B. $\frac{1}{x\log x}$
• C. $\frac{1}{\log x}$
• D. $e^y$

Answer 1

The correct option is A

$\frac{1}{x}$

Find the $\frac{dy}{dx}$:

Given that, $y=\mathrm{loglog}x$

Differentiate $y$ with respect to $x$ using chain rule we get:

$\frac{dy}{dx}=\frac{1}{\log x}·\frac{1}{x}$

And $y=\mathrm{loglog}x$$\Rightarrow e^y=\log x$

By substituting value we have:

$\begin{array}{rcl}\frac{dy}{dx}& =& \frac{1}{e^y}·\frac{1}{x}\\ e^y\frac{dy}{dx}& =& \frac{1}{x}\end{array}$

Hence, option A is correct.