Quotient Rule Practice - Grade 10 Calculus
Practice applying the quotient rule for differentiation with various functions, including polynomial, rational, and trigonometric examples.
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Quotient Rule Practice
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Apply the quotient rule to find the derivative of each function. Simplify your answers where possible.
1. Find the derivative of the function f(x) = (3x - 2) / (x^2 + 1).
2. Differentiate g(x) = (e^x) / (sin x).
For the function h(x) = (x^3 + 5) / (cos x), let u = and v = . Then u' = and v' = .
4. Which of the following is the correct application of the quotient rule for y = u/v?
y' = (u'v + uv') / v^2
y' = (u'v - uv') / v^2
y' = (uv' - u'v) / v^2
y' = (u'v - uv') / u^2
5. The quotient rule is always necessary when differentiating a fraction.
True
False
6. Find the derivative of f(x) = (x^2 - 4) / (x^2 + 4) and simplify your answer.
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