Compute the indicated derivative

Question

d/dx [(x^3+5x)(x^2-x).... at x=2? 

 

 

Answer 1

The function f(x) = (x³ + 5x)(x² - x)

y = (x³)(x²) + 5x(x²) + (x³)(- x) + (5x)(- x)

y = x⁵ + 5x³ - x⁴ - 5x²

Apply derivative on each side with respect of x.

d/dx(y) = x⁵ + 5x³ - x⁴ - 5x²

Apply the formula d/dx(xⁿ) = nx^n-1

y' = 5x⁴ + 15x² - 4x³ - 10x

y' at x = 2.

y' = 5(2)⁴ + 15(2)² - 4(2)³ - 10(2)

y' = 80 + 60 - 32 - 20

y'(2) = 88.