Find F ' (x) given that

Question

F(x)= (2x³+3x²-5)(5x²-2x+1)

Answer 1

F(x) = (2x^3+3x^2 -5)(5x^2 -2x +1)

F(x) = 2x^3 +3x^2 -5 + 10x^5 + 15x^4-25x^2 -4x^4 -6x^3 +10x

= 10x^5 +11x^4 -4x^3 -22x^2 +10x -5

F'(x) = 50x^4 + 44x^3 -12x^2 -44x +10

Answer 2

Use the product rule (and power rule (xⁿ)' = nx^n-1) to find F'(x):

F'(x) = (2x³ + 3x² - 5)' • (5x² - 2x + 1) + (2x³ + 3x² - 5) • (5x² - 2x + 1)'

........= (6x² + 6x)(5x² - 2x + 1) + (2x³ + 3x² - 5)(10x - 2)