NIMCET 2017 — Mathematics PYQ

Concept:
Chain rule: $\frac{d}{dx}[f(g(x))]=f^{\prime }(g(x))g^{\prime }(x)$

Calculation:
Here, -log (log x), x > 1
Let, log x = y
Differentiating with respect to x, we get
$\Rightarrow \frac{dy}{dx}=\frac{1}{x}$ ... (1)
Now, -log (log x) = -log y
$\frac{d}{dx}(-\log y)=-\frac{1}{y}\frac{dy}{dx}$
$=-\frac{1}{x\log x}$ ... (from (1))