What is the answer?

Question

Find h'(-3) if h = f · g, f(x)= -5x²-9 and the equation of the tangent line of g at -3 is y = -3x-1

Answer 1

By the Chain Rule h '(-3) = f '(g(-3)) g '(-3)

The equation of the tangent line of g at -3 is y = -3x-1, so

(a) g(-3) = -3(-3) - 1 = 8; g '(-3) = (-3x-1) ' = -3

Next, f(x) = -5x² - 9, so f '(x) = -10x

Then f '(g(-3)) = f '(8) = -10(8) = -80

Finally, h '(-3) = (-80)(-3) = 240

Answer 2

g'(x) = -3x -1

Determine g(x).

Determine h(x)

Determine h'(x)

Determine h'(-3)