How do you find the derivative of arctan (cos x)?

1 Answer
Jim G.
Mar 3, 2016

(-sinx)/(1 + cos^2x)

Explanation:

using thecolor(blue)" chain rule "

d/dx[f(g(x))] = f'(g(x)) . g'(x)

and the standard derivative d/dx(tan^-1 x) = 1/(1+x^2)

d/dx[tan^-1(cosx)] = 1/(1+ cos^2 x) . d/dx(cosx)

= (-sinx)/(1 + cos^2 x)

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