Question

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

Answer 1

`dy/dx=-45x^2(-5x^3-3)^2`

Explanation:

To 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)|)))`

`"let " u=-5x^3-3rArr(du)/(dx)=-15x^2`

`"and " y=u^3rArr(dy)/(du)=3u^2`

`rArrdy/dx=3u^2(-15x^2)`

change u back into terms of x

`rArrdy/dx=-45x^2(-5x^3-3)^2`