Question:
Derivative of \( x^2 \) with respect to \( x^3 \), is:
Derivative of \( x^2 \) with respect to \( x^3 \), is:
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When differentiating with respect to a different variable, apply the chain rule and adjust for the powers of the variables.
Updated On: Jan 13, 2026
- \( \frac{2}{3x} \)
- \( \frac{3x}{2} \)
- \( \frac{2x}{3} \)
- \( 6x^5 \)
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The Correct Option is A
Solution and Explanation
We are asked to differentiate \( x^2 \) with respect to \( x^3 \), so we need to use the chain rule. \[ \frac{d}{dx} \left( \frac{x^2}{x^3} \right) = \frac{d}{dx} \left( x^{2 - 3} \right) = \frac{d}{dx} \left( x^{-1} \right) \] \[ \frac{d}{dx} \left( x^{-1} \right) = -x^{-2} = \frac{2}{3x} \]
Step 2: Verify the options
The correct derivative is \( \frac{2}{3x} \), matching option (A).
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