Question

How do you differentiate `y=(1-x^2)^10`?

Answer 1

`dy/dx=-20x(1-x^2)^9`

Explanation:

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

`color(red)(bar(ul(|color(white)(2/2)color(black)(dy/dx=(dy)/(du)xx(du)/(dx))color(white)(2/2)|)))`

`"let "u=1-x^2rArr(du)/(dx)=-2x`

`"then "y=u^10rArr(dy)/(du)=10u^9`

`rArrdy/dx=10u^9.(-2x)`

convert u back into terms of x and simplify.

`rArrdy/dx=-20x(1-x^2)^9`