Please I need help with the calculus question below

Question

If h(x) = f^2(x) - g^2(x), f'(x) = -g(x) and g'(x) = f(x), then h'(x) is?

From the following choose the correct answer to the question above:

A: 0

B: 1

C: -4f(x)g(x)

D: (-g(x))^2 - (f(x))^2

Answer 1

h(x) = [ f(x)]² - [g(x)]²

h'(x) = 2[f(x)]f'(x) - 2[g(x)]g'(x) - power rule followed by the chain rule for both terms

h'(x) = 2[f(x)][-g(x)] - 2[g(x)]f(x) - substitution from given

h'(x) = -4f(x)g(x) -- simplify

Answer 2

The answer is C.

Remember the chain rule!!!!

Answer 3

First h(x) = (f(x))² - (g(x))²

Rewrite this as h(x) = f(x)*f(x) - g(x)*g(x)

take the derivative of both sides using the product rule to get:

h'(x) = f(x)*f '(x) + f(x)*f '(x) - [g(x)*g'(x) + g(x)*g'(x)]

Simplify

h'(x) = 2f(x)f '(x) - 2g(x)g'(x)

Now make a substitution

h'(x) = 2f(x)[-g(x)] - 2g(x)[f(x)]

Finally solve for h'(x)