Question

How do you use the chain rule to differentiate `y=(-3x+7)^5`?

Answer 1

`dy/dx=-15(-3x+7)^4`

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(blue)"-------------------------------------------"`

let `u=-3x+7rArr(du)/dx=-3`

and `y=u^5rArr(dy)/(du)=5u^4`
`color(blue)"--------------------------------------------"`
substitute these values into (A) changing u back into terms of x.

`rArrdy/dx=5(-3x+7)^4.(-3)=-15(-3x+7)^4`