Derivative of x^2 w.r.t. x^3 is: - Mathematics MCQ Mathematics Mock Test - 5 2026 | ExamTest.live

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Derivative of x^{2} w.r.t. x^{3} is:

Solution & Step-by-step Explanation

Let u = x^{2} and v = x^{3} . We need to find \frac{d u}{d v} . \frac{d u}{d x} = 2 x \frac{d v}{d x} = 3 x^{2} Using the chain rule: \frac{d u}{d v} = \frac{\frac{d u}{d x}}{\frac{d v}{d x}} = \frac{2 x}{3 x ^{2}} = \frac{2}{3 x}

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Derivative of x^{2} w.r.t. x^{3} is:

\frac{1}{x}

x

0

\frac{2}{3 x}

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