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Question Number 164366 by Zaynal last updated on 16/Jan/22

$$\frac{\mathit{d}}{\mathit{d}\mathit{x}}\left({\mathit{e}}^{\mathit{t}\mathit{a}\mathit{n}\left(\mathit{x}\right)}\right)$$$$\{\mathit{Z}.\mathbf{A}\}$$

Commented by cortano1 last updated on 16/Jan/22

$$y=e^{\tan x}$$$$\ln y=\tan x$$$$\frac{y^{\prime }}{y}=\sec {}^{2}x$$$$\frac{dy}{dx}=\sec {}^{2}x\left(e^{\tan x}\right)$$

Answered by muneer0o0 last updated on 16/Jan/22

$$\frac{\mathit{d}}{\mathit{d}\mathit{x}}\left({\mathit{e}}^{\mathit{t}\mathit{a}\mathit{n}\left(\mathit{x}\right)}\right)=\frac{d\left(e^{\tan x}\right)}{d\left(\tan x\right)}\times \frac{d\left(\tan x\right)}{dx}=e^{\tan x}{\sec }^{2}x$$

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