Product rule

Definition

The product rule is a differentiation rule used to find the derivative of the product of two functions. It states that if $u(x)$ and $v(x)$ are differentiable functions, then the derivative of their product is given by $(uv)' = u'v + uv'$.

5 Must Know Facts For Your Next Test

1. The formula for the product rule is $(uv)' = u'v + uv'$.
2. It applies to the product of two differentiable functions.
3. To use the product rule, you need to know how to differentiate each function separately.
4. If either function is not differentiable at a point, the product rule cannot be applied at that point.
5. The order in which you multiply derivatives does not matter: $u'v + uv' = v'u + vu'$.

Review Questions

• What is the product rule formula?
• Can you apply the product rule if one of the functions is not differentiable?
• How do you find the derivative of $f(x) = x^2 e^x$ using the product rule?

Related terms

Quotient Rule: A differentiation rule used to find the derivative of the quotient of two functions. The formula is $(\frac{u}{v})' = \frac{u'v - uv'}{v^2}$.

Chain Rule: A differentiation rule used to find the derivative of a composite function. The formula is $(f(g(x)))' = f'(g(x)) g'(x)$.

Power Rule: A basic differentiation rule used to find the derivative of a power function. The formula is $(x^n)' = nx^{n-1}$.