CA Foundation P3 · Chapter 8 · Question 2 of 9
The derivative of x²eˣ with respect to x is:
Test yourself: pick an answer
Reveal answer & explanation
Correct answer: B) eˣ(x² + 2x)
Explanation
By the product rule, d/dx(uv) = u'v + uv'. With u = x², v = eˣ: 2x·eˣ + x²·eˣ = eˣ(x² + 2x). Differentiating only one factor gives 2xeˣ.
More Basic Applications of Differential and Integral Calculus in Business and Economics MCQs
- 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:
- Q8The demand function for a product is q = 100 − 2p. The price elasticity of demand (in absolute value) at p = 20 is: