Suppose f(2)=5, f'(2)=4, f(10)=9, f'(10)=7, g(2)=6, g'(2)=-5, and H(x)=f(x^2+g(x)). Find dH/dx||||x=2. H'(2)=?

Question

need help

Answer 1

H(x) = f(x² + g(x))

 

H'(x) = f'(x² + g(x))(x² + g(x))'

 

          = f'(x² + g(x))(2x + g'(x))

 

H'(2) = f'(2² + g(2))(4 + g'(2))

 

          = f'(4 + 6)(4 + (-5)) = f'(10)(-1) = (7)(-1) = -7