Product Rule Practice Worksheet
A Grade 12 Calculus worksheet focusing on the product rule for differentiation, including various function types and applications.
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Product Rule Practice Worksheet
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Read each question carefully and apply the product rule to find the derivative of the given functions. Show all your work for full credit.
Find the derivative of each function using the product rule.
1. f(x) = (3x^2 + 5)(2x - 1)
2. g(x) = (x^3 - 2x)(e^x)
Complete the missing parts of the product rule application.
1. If y = (x^2 + 1)(sin x), then dy/dx = (x^2 + 1) + (sin x) .
2. If h(t) = (ln t)(t^4), then h'(t) = (ln t) + (t^4) .
1. Which of the following is the correct derivative of y = x * cos(x)?
cos(x) + x sin(x)
cos(x) - x sin(x)
-sin(x)
sin(x) - x cos(x)
Determine if the following statements are True or False.
1. The product rule states that if h(x) = f(x)g(x), then h'(x) = f'(x)g'(x).
True
False
Given f(x) = x^2 and g(x) = sqrt(x), find the derivative of h(x) = f(x)g(x) using the product rule. Express your answer in simplest form.