How do you differentiate arctan(sinx)?

1 Answer
t0hierry
Feb 8, 2017

y' = 1/(1 + sin^2 x) cos x

Explanation:

It is the derivative of a function arctan, of a function sin. It is equal to the derivative of the first function arctan, expressed in terms of its argument, multiplied by the derivative of the argument with respect to x.

The derivative of arctan u is 1/(1 + u^2). When u is sin(x) it is simply 1/(1 + sin^2 x). The derivative of sin(x) is cosx. Multiplying both yields

y' = 1/(1 + sin^2 x) cos x

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