F(5)=7, f’(5)=3, f(20)=1, f’(20)=-8 and H(x)=f(x^2-5). Find dH/dx|x=5

Answer 1

First we start by differentiating the function H(x) with respect to x:

dH/dx = d/dx [H(x)] = d/dx [f(x^2-5)]

= (2x)*f'(x^2-5)

Next, we plug 5 in for x in our equation for dH/dx:

dH/dx | x=5 = (2*5)*f'(5^2-5)

= (10)*f'(20)

= (10)*(-8)

= -80 (Answer)