Quotient Rule Practice Worksheet
A Grade 12 Calculus worksheet focusing on applying the quotient rule for differentiation.
Includes
Standards
Topics
Quotient Rule Practice
Name:
Date:
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Read each question carefully and show all your work. Apply the quotient rule to differentiate the following functions.
1. Find the derivative of $f(x) = \frac{x^2 + 1}{x - 3}$.
2. Differentiate $y = \frac{\sin x}{x^2}$.
3. Determine $\frac{dy}{dx}$ for $y = \frac{e^x}{x+1}$.
4. If $f(x) = \frac{2x}{x^2 + 1}$, what is $f'(1)$?
$0$
$1$
$-1$
$2$
5. The quotient rule states that if $h(x) = \frac{f(x)}{g(x)}$, then $h'(x) = \frac{g(x)f'(x) - f(x)g'(x)}{ }$.
6. The derivative of $\frac{1}{x}$ using the quotient rule is $-\frac{1}{x^2}$.
True
False
7. Find the derivative of $f(x) = \frac{\ln x}{e^{2x}}$.
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