Practice Quotient Rule (3.2.4) - Calculus

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6 sample questions

Question 1.
Differentiate $f(x) = \frac{2x}{x^2 + 3}$ using the Quotient Rule.
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Identify \$ g(x) \$ and \$ h(x) \$ before differentiating.
Question 2.
Find the derivative of $f(x) = \frac{x^3}{x+1}$ .
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Remember the structure of the Quotient Rule: numerator's derivative multiplied by denominator minus the numerator multiplied by the denominator's derivative.
3Question 3.
What does the Quotient Rule calculate?
- The derivative of a sum of functions
- The derivative of the product of functions
- The derivative of a quotient of functions
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Focus on the nature of the functions involved.
4Question 4.
Using the Quotient Rule, how do we represent $f'(x)$ ?
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Keep in mind the structure of the rule you learned.
Question 5.
Differentiate the function $f(x) = \frac{x^2 + 1}{sin(x)}$ and simplify your answer.
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Be careful with trig functions as derivatives influence each other.
Question 6.
For the function $f(x) = \frac{x^3 + cos(x)}{x - 2}$ , determine $f'(x)$ .
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Simplifying complex expressions could become tricky; keep your work organized.

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