Question

$If y = sin (log x), then \frac{d y}{d x} =__________$

$\frac{1}{x} cos (log x)$
$\frac{1}{x} sin (log x)$
$0$
$1$

Answer: $\frac{1}{x} cos (log x)$

Solution :-

Given that y = sin (log x)

Differentiate with respect to $x$ , we get

\begin{aligned} \frac{d y}{d x} & = & \frac{d (sin (log x))}{d x} \\ = & \frac{d (sin (log x))}{d (log x)} \cdot \frac{d (log x)}{d x} (after applying chain rule of derivative) \\ = & cos (log x) \cdot \frac{1}{x} (∵ \frac{d (sin x)}{d x} = cos x and \frac{d (log x)}{d x} = \frac{1}{x}) \\ ∴ \frac{d y}{d x} & = & \frac{1}{x} cos (log x) \cdot \end{aligned}

So, correct answer is option-1, $\to \frac{1}{x} cos (log x)$

#Differentiation #BSEB PYQ 2017 #Mathematics #BSEB PYQs