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

1 Answer

Aug 6, 2015

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

Explanation:

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 #

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