Find f '(−5), if f(x) = (−4x^2 − 2x)(−x^2 − 9).

Answer 1

f(x) = (-4x² - 2x)(-x² - 9)

Option 1 is to use the Product Rule. Option 2 is to multiply it out:

f(x) = 4x⁴ + 2x³ + 36x² + 18x

f '(x) = 16x³ + 6x² + 72x + 18

To find f '(-5) just plug in x = -5.