CUET · MATHS · PYQ PAPER 2025
If \(y=\frac{1}{\sqrt[3]{1-x^3}}\), then \(\frac{d y}{d x}\) is equal to :
- A \(x\left(1-x^3\right)^{-\frac{4}{3}}\)
- B \(x^2\left(1-x^3\right)^{-\frac{4}{3}}\)
- C \(\left(1-x^3\right)^{-\frac{4}{3}}\)
- D \(-x^2\left(1-x^3\right)^{-\frac{4}{3}}\)
Answer & Solution
Correct Answer
(B) \(x^2\left(1-x^3\right)^{-\frac{4}{3}}\)
Step-by-step Solution
Detailed explanation
\(y = (1-x^3)^{-\frac{1}{3}}\) \(\frac{d y}{d x} = -\frac{1}{3}(1-x^3)^{-\frac{4}{3}}(-3x^2)\) \(\frac{d y}{d x} = x^2(1-x^3)^{-\frac{4}{3}}\)
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