f(-8)=9, f’(-8)=5, g(-8)=0, g’(-8)=8 and H(x)= square root of (f(x)+g(x)) Find dH/dx|x=-8

Answer 1

dH/dx = 1/2(f(x) + g(x))^-1/2(f'(x) + g'(x)) by chain rule.

Then H'(- 8) = 1/2( 9 + 0)^-1/2(5 + 8) = 1/2·1/3·13 = 13/6