Product Rule Practice Worksheet
Practice applying the product rule for differentiation in various calculus problems.
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Product Rule Practice
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Apply the product rule to find the derivative of each function. Show all your work.
1. Find the derivative of $f(x) = (x^2 + 3)(2x - 1)$.
2. Differentiate $y = (3x^4 - 2x)(x^3 + 5x^2)$.
3. The product rule states that if $h(x) = f(x)g(x)$, then $h'(x) = f'(x)g(x) +$ .
4. If $f(x) = x^3$ and $g(x) = \sin(x)$, then $f'(x) = 3x^2$ and $g'(x) = $ .
5. The derivative of $f(x) = x^2 \cos(x)$ is $f'(x) = 2x \cos(x) + x^2 \sin(x)$.
True
False
6. The product rule can be used to differentiate $f(x) = \frac{x^2}{e^x}$.
True
False
7. Which of the following functions requires the product rule for differentiation?
$f(x) = x^5 + 3x$
$f(x) = \frac{x^2}{x-1}$
$f(x) = (x^2 - 4)(e^x)$
$f(x) = \ln(x)$
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