Calculus

Derivative: Product Rule

Formula

(fg)' = f'g + fg'

What is Derivative: Product Rule?

The product rule is used to differentiate the product of two functions. The derivative of f times g equals f-prime times g plus f times g-prime.

Variables

f
f, g — Two functions of x
f
f' — Derivative of f
g
g' — Derivative of g

Worked Examples

Example 1

Find the derivative of x² × sin(x).

Solution:

f = x², g = sin(x). (fg)' = 2x·sin(x) + x²·cos(x)

Frequently Asked Questions

Related Formulas

Derivative: Power Rule

d/dx [xⁿ] = n × xⁿ⁻¹

Derivative: Quotient Rule

(f/g)' = (f'g − fg') / g²

Derivative: Chain Rule

d/dx [f(g(x))] = f'(g(x)) × g'(x)

Integral: Power Rule

∫xⁿ dx = xⁿ⁺¹/(n+1) + C (n ≠ −1)

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