What is the derivative of $y = sin (tan 2 x)$ $y=sin(tan2x)$ ?

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What is the derivative of $y = sin (tan 2 x)$ $y=sin(tan2x)$ ?

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Answer 1 · 2018-06-18T15:06:23

$2 {sec}^{2} 2 x cos tan 2 x$ $2sec^2 2xcostan2x$

Explanation:

Use the chain rule:
$\frac{d}{d x} [sin tan 2 x] = cos tan 2 x \cdot \frac{d}{d x} [tan 2 x]$ $d/dx[sintan2x]=costan2x*d/dx[tan2x]$
$= cos tan 2 x \cdot {sec}^{2} 2 x \cdot \frac{d}{d x} [2 x]$ $=costan2x*sec^2 2x*d/dx[2x]$
$= 2 {sec}^{2} 2 x cos tan 2 x$ $=2sec^2 2xcostan2x$

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What is the derivative of $y = sin (tan 2 x)$ $y=sin(tan2x)$ ?

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What is the derivative of y=sin(tan2x)y=sin(tan2x)?

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What is the derivative of $y = sin (tan 2 x)$ $y=sin(tan2x)$ ?