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provide solution for RD Sharma maths class 12 chapter Differentiation exercise  10.2 question 6

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Answer: e^{\tan x} \times \sec ^{2} x

Hint:You must know the rules of solving derivation of exponential function and trigonometric function.

Given: e^{\tan x}


y=e^{\tan x}

Differentiating with respect to x,

\begin{aligned} &\frac{d y}{d x}=\frac{d}{d x} e^{\tan x} \\ &\frac{d y}{d x}=e^{\tan x} \frac{d}{d x}(\tan x) \end{aligned}                   [ using chain rule] and \frac{d}{d x}(\tan x)=\sec ^{2} x

\frac{d y}{d x}=e^{\tan x} \times \sec ^{2} x

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