Question

How do you use the chain rule to differentiate `y=4(x^3+1)^(1/2)`?

Answer 1

`(6x^2)/(x^3+1)^(1/2)`

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^3+1rArr(du)/(dx)=3x^2`

and `y=4u^(1/2)rArr(dy)/(du)=2u^(-1/2)`

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

`dy/dx=2u^(-1/2)xx3x^2=(6x^2)/(x^3+1)^(1/2)`