How do you take the derivative of $tan^2(5x)$ ?

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Answer 1 · 2015-08-06T13:09:39

$= 10tan 5x sec^2 5x$

Let $t = 5x$ .

$frac{d}{dx}tan^2 5x = frac{dt}{dx}frac{d}{dt}tan^2 t$ .

Product rule: $frac{d}{dt}tan^2 t = 2tan t\frac{d}{dt}tan t$ .
Now $\frac{d}{dt} tan t = sec^2 t$ .

Hence $frac{d}{dx}tan^2 5x = 10tan 5x sec^2 5x$

How do you take the derivative of tan^2(5x)tan^2(5x)?