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 $(uv)' = u'v + uv'$.
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The formula for the product rule is $(uv)' = u'v + uv'$.
It applies to the product of two differentiable functions.
To use the product rule, you need to know how to differentiate each function separately.
If either function is not differentiable at a point, the product rule cannot be applied at that point.
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 $(x^n)' = nx^{n-1}$.