Finding Polynomial Derivatives

Calculus 1 · Axiom Academy

EXAMPLE Finding Polynomial Derivatives Apply the power rule to differentiate a polynomial term by term. Find f'(x) for the polynomial f(x) = 4x^3 - 2x^2 + 5x + 7 . Nice work — you differentiated a polynomial term by term using the power rule. Power Rule: — multiply by the exponent, then reduce the exponent by 1 . Constant Multiple Rule: a coefficient rides along unchanged, e.g. . Sum / Difference Rule: differentiate each term separately and keep the signs. Linear term: — the coefficient becomes the derivative. Constants vanish: , so f'(x) = 12x^2 - 4x + 5 . The power rule is the workhorse behind differentiating almost every function you'll meet.

This is the written version of the interactive lesson above. See the full Calculus 1 course.