First slide

Derivatives

Question

$If y = \exp \{\sin^{2} x + \sin^{4} x + \sin^{6} x + \dots .\} then \frac{d y}{d x} =$

Moderate

A

$e^{\tan^{2} x}$
B

$e^{\tan^{2} x} \sec^{2} x$
C

$2 e^{\tan^{2} x} \tan x \sec^{2} x$
D

$e^{\tan^{2} x} \tan x \sec^{2} x$

Solution

$y = e^{\frac{\sin^{2} x}{1 - \sin^{2} x}} = e^{\tan^{2} x} \Rightarrow \frac{d y}{d x} = e^{\tan^{2} x} \cdot 2 \tan x \sec^{2} x$

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