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

1 Answer
Sep 8, 2016

(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)