Quotient Rule Practice Worksheet
Practice applying the quotient rule for differentiation with various functions, including trigonometric and exponential functions.
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Quotient Rule Practice
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Apply the quotient rule to find the derivative of each function. Show all your work.
1. Find the derivative of $f(x) = \frac{x^2 + 1}{x - 3}$.
2. Differentiate $g(x) = \frac{\sin(x)}{\cos(x) + 1}$.
3. The quotient rule states that if $h(x) = \frac{f(x)}{g(x)}$, then $h'(x) = \frac{g(x)f'(x) - f(x)g'(x)}{ }$.
4. When applying the quotient rule, it is often helpful to identify the 'high' function as and the 'low' function as .
5. Which of the following is the correct derivative of $y = \frac{e^x}{x^2}$?
$y' = \frac{xe^x - 2e^x}{x^3}$
$y' = \frac{x^2e^x - 2xe^x}{x^4}$
$y' = \frac{e^x - 2x}{x^4}$
$y' = \frac{x^2e^x - 2xe^x}{x^2}$
6. Find $\frac{dy}{dx}$ for $y = \frac{\ln(x)}{x^3}$.
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