Find f'(x) (the derivative of f(x)) if f(x) = 7x^3 - 2x^2 + 4x - 5.

Answer 1

Just use the power rule. The power rule says to take the exponent, multiply it by the coefficient, and reduce the exponent by 1.

For the first term 7x³, multiply the exponent "3" by the coefficient "7" (to get "21") and reduce the exponent by 1 making it "2" so the derivative is 21x²

Repeat for the other terms (note that derivatives of constants (like -5) will be zero) to get f '(x) = 21x² - 4x + 4

Answer 2

f'(x) = 7(3)x^3-1-2(2)x^2-1+4(1)x^1-1 -5(0)

f'(x) = 21x²-4x+4