f(-3)=3, f’(-3)=3, g(-3)=4, g’(-3)=-6 and H(x)=f(x)e^(g(x)). Find the derivative dH/dx|x=-3

Answer 1

f(-3) = 3

f’(-3) = 3

g(-3) = 4

g’(-3) = -6

H(x) = f(x)e^g(x)

Differentiate H(x) using the chain rule and product rule:

H'(x) = f(x) g'(x) e^g(x) + f'(x) e^g(x)

Find the derivative dH/dx at x = -3:

H'(-3) = f(-3) g'(-3) e^g(-3) + f'(-3) e^g(-3) = (3) (-6) e⁴ + (3) e⁴ = -18e⁴ + 3e⁴ = -15e⁴