How do you find the derivative of sin(cosx)?

1 Answer
Jim G.
Dec 3, 2016

-sinxcos(cosx)

Explanation:

differentiate using the color(blue)"chain rule"

color(orange)"Reminder " color(red)(bar(ul(|color(white)(2/2)color(black)(dy/dx=(dy)/(du)xx(du)/(dx))color(white)(2/2)|)))to(A)

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

"and " y=sinurArr(dy)/(du)=cosu

Substitute into ( A), changing u back to terms of x.

rArrdy/dx=cosuxx(-sinx)=-sinxcos(cosx)

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