What is the derivative of f(x) = (3x - 2)^5?
Correct answer: A. 15(3x - 2)^4
- A. 15(3x - 2)^4
- B. 5(3x - 2)^4
- C. 15(3x - 2)^5
- D. (3x - 2)^4
Explanation
The chain rule multiplies the outer derivative by the derivative of 3x - 2. Therefore, f'(x) = 5(3x - 2)^4 × 3 = 15(3x - 2)^4.
Report an error
The more specific you are, the faster it gets fixed. A source beats an opinion.
Prefer email? [email protected]
About Differentiation and Optimisation
Differentiation covers gradients, standard derivative rules, the product and quotient rules, the chain rule, stationary points and rates of change. Optimisation uses first and second derivatives to classify maxima and minima, while applications include tangent and normal lines, marginal quantities and related rates.
Practise Differentiation and Optimisation
30 free Differentiation and Optimisation MCQs from Quantitative Methods, each with the correct answer and an explanation. Unlimited attempts, no account needed.
Discussion
Stuck on an option, or know a faster way to get there? Ask or explain it here.
No comments yet. Be the first to explain this one.
Exams that ask Quantitative Methods questions like this
Quantitative Methods is on this paper prepared for on TestUstad, and all of them draw the same bank, so this question is worth knowing for it.
More Differentiation and Optimisation questions
If f(x) = (x^2 + 1)e^x, what is f'(0)?
What is the absolute maximum value of f(x) = x³ - 3x on the interval [-2, 2]?
The curve x² + y² = 25 passes through the point (3, 4). What is dy/dx at that point?
If f'(1) = 0 and f''(1) = 0, what conclusion follows from the second derivative test?
For f(x) = x^3 - 3x^2 + 2, on which interval is the graph concave upward?
A closed cylinder has a fixed volume. At the dimensions that minimise its total surface area, how are its height h and radius r related?