Question

How do you find the derivative of `Y= ( 2x + 9 ) sqrt(x^2 - 4)`?

Answer 1

`Y'=(2x+9)*x/(sqrt(x^2-4))+2*sqrt(x^2-4)`

Explanation:

Let `f(x)=2x+9` and `g(x)=sqrt(x^2-4)`. Their derivatives are:
`f'(x)=2` and `g'(x)=1/2(x^2-4)^(-1/2)*2x=x/(sqrt(x^2-4))`

The Product Rule says that

`Y'=f(x)g'(x)+f'(x)g(x)`

`Y'=(2x+9)*x/(sqrt(x^2-4))+2*sqrt(x^2-4)`