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

1 Answer
Aug 4, 2015

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)