Question

What is the derivative of `sqrt(4-x^2)`?

Answer 1

`(-x)/(sqrt(4-x^2))`

Explanation:

Differentiate using a combination of `color(blue)"power and chain rule"`

`color(orange)"Reminder of chain rule"`

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

let `u=4-x^2rArr(du)/(dx)=-2x`

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

substitute these values into (A) converting u back into terms of x.

`rArrdy/dx=1/2u^(-1/2).(-2x)=(-x)/(sqrt(4-x^2))`