What is the derivative of $y = sin(tan(5x))$ ?

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Answer 1 · 2015-12-16T03:03:31

$y'=5sec^2(5x)cos(tan(5x))$

Use the chain rule. The first overriding issue is the tangent function inside the sine function.

$y'=cos(tan(5x))d/dx[tan(5x)]$

Next, use chain rule again to find the derivative of the tangent function.

$d/dx[tan(5x)]=sec^2 5xd/dx[5x]=5sec^2(5x)$

Multiply this back in to find $y'$ .

$y'=5sec^2(5x)cos(tan(5x))$

What is the derivative of y = sin(tan(5x))y = sin(tan(5x))?