CA Foundation P3 · Chapter 8 · Question 1 of 9
The derivative of y = x⁵ + 3x² − 7 with respect to x is:
Test yourself: pick an answer
Reveal answer & explanation
Correct answer: D) 5x⁴ + 6x
Explanation
Using d/dx(xⁿ) = nxⁿ⁻¹ and d/dx(constant) = 0: dy/dx = 5x⁴ + 3(2x) − 0 = 5x⁴ + 6x. Keeping the constant −7 is a common error.
More Basic Applications of Differential and Integral Calculus in Business and Economics MCQs
- Q3The total cost function of a firm is C = 0.5x² + 20x + 400 (in ₹). The marginal cost when x = 30 units is:
- Q4The derivative of y = log(3x² + 1) with respect to x is:
- Q5The profit function of a firm is P = −2x² + 120x − 500 (in ₹). The maximum profit is:
- Q6∫(6x² − 4x + 5) dx is equal to:
- Q7The value of the definite integral ∫ from 1 to 3 of (2x + 1) dx is: