Question

What is the derivative of this function `cos x^5`?

Answer 1

`-5x^4sin(x^5)`

Explanation:

differentiate using the `color(blue)"chain rule"`

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

let `u=x^5rArr(du)/(dx)=5x^4`

and `y=cosurArr(dy)/(du)=-sinu`

substitute these values into (A) change u back to terms of x.

`rArrdy/dx=-sinuxx5x^4=-5x^4sin(x^5)`