Question

Derivative help?

(x^2+3x+6)(15-2x^2)

 

Answer 1

The function f(x) = (x² + 3x + 6)(15 - 2x²)

= x²(15) + x² (- 2x²) + 3x(15) + 3x(- 2x²) + 6(15) + 6(- 2x²)

= 15x² -  2x⁴ + 45x - 6x³ + 90 - 12x²

f(x) = - 2x⁴ - 6x³ + 3x² + 45x + 90

Apply derivative on each side with respect to x.

Recall the formulae :

d/dx(xⁿ) = nx^n-1

d/dx(x) = 1

d/dx(constant) = 0

f'(x) = - 8x³ - 18x² + 6x + 45.