Find E'(8). E(x) = (0.001x − 0.062)(−0.18x2 + 8.2x − 200)

Question

E(x) = (0.001x − 0.062)(−0.18x² + 8.2x − 200)

Find E'(8). (Give an exact answer. Do not round.) 

E' (x) = ?

Answer 1

This can be done one of two ways. You can either multiply the equation out and take the derivative using the power rule, or use the product rule and take derivative as it stands. I prefer the later.

so if a product of two functions, fg, then derivative is f'g+g'f

E'(x) = (0.001)((−0.18x² + 8.2x − 200) + (-.36x + 8.2)(0.001x-0.062). Then evaluate this function at x = 8. I come up with -0.4332.