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

1 Answer
Jim G.
Sep 1, 2016

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

Explanation:

differentiate using the color(blue)"chain rule"

color(red)(|bar(ul(color(white)(a/a)color(black)(dy/dx=(dy)/(du)xx(du)/(dx))color(white)(a/a)|)))........ (A)

color(orange)"Reminder " color(red)(|bar(ul(color(white)(a/a)color(black)(d/dx(arctanx)=1/(1+x^2))color(white)(a/a)|)))

let u=cosxrArr(du)/(dx)=-sinx

and y=arctanurArr(dy)/(du)=1/(1+u^2)

substitute these values into (A) changing u back to x.

rArrdy/dx=1/(1+u^2)xx(-sinx)=(-sinx)/(1+cos^2x)

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