Differentiate x^2 with respect to x^3. - Vidyadip

Question

Differentiate $x^2$ with respect to $x^3$.

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Answer

Let $u = x^2$ and $v = x^3$
$\Rightarrow\frac{\text{du}}{\text{dx}}=2\text{x and }\frac{\text{dv}}{\text{dx}}=3\text{x}^2$
$\therefore\frac{\text{du}}{\text{dv}}=\frac{\frac{\text{du}}{\text{dx}}}{\frac{\text{dv}}{\text{dx}}}=\frac{2\text{x}}{3\text{x}^2}=\frac{2}{3\text{x}}$

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