How do you find the derivative of the function $y = sin (tan (5 x))$ $y = sin(tan(5x))$ ?

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Answer 1 · 2016-05-24T07:59:09

$cos (tan (5 x)) {sec}^{2} (5 x) 5$ $\cos (\tan (5x))\sec ^2(5x)5$

$\frac{d}{d x} (sin (tan (5 x)))$ $\frac{d}{dx}(\sin (\tan (5x)))$

Applying chain rule,
$\frac{d f (u)}{d x} = \frac{d f}{d u} \cdot \frac{d u}{d x}$ $\frac{df(u)}{dx}=\frac{df}{du}\cdot \frac{du}{dx}$

Let $tan (5 x)$ $tan(5x)$ = u

We know,
$\frac{d}{d u} (sin (u)) = cos (u)$ $\frac{d}{du}(\sin(u))=\cos(u)$

$\frac{d}{d x} (tan (5 x)) = {sec}^{2} (5 x) 5$ $\frac{d}{dx}(\tan(5x))=\sec ^2(5x)5$

So,
$= cos (u) {sec}^{2} (5 x) 5$ $=\cos(u)\sec ^2(5x)5$

Substituting back, $tan (5 x)$ $tan(5x)$ = u

$= cos (tan (5 x)) {sec}^{2} (5 x) 5$ $=\cos(\tan(5x))\sec ^2(5x)5$

How do you find the derivative of the function y = sin(tan(5x))y=sin(tan(5x))y = sin(tan(5x))?