Suppose that f(5)=−7, g(5)=2, f′(5)=9, and g′(5)=−5. Find (f^2+g^2)′(5).

Question

Suppose that f(5)=−7, g(5)=2, f′(5)=9, and g′(5)=−5. Find (f²+g²)' (5).

Answer 1

Applying the chain rule we obtain the expression 2f(5)f’(5)+2g(5)g’(5)=-14(9)-4(5)=-126-20=-146.