The differential coefficient of {x^3} with re | vedclass

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Question

(B) Let $u = x^3$ and $v = x^2$. We need to find the derivative of $u$ with respect to $v$,which is $\frac{du}{dv}$. Using the chain rule,$\frac{du}{d

Vedclass · Accepted Answer

${{3x} \over 2}$

Vedclass · Answer

(B) Let $u = x^3$ and $v = x^2$. We need to find the derivative of $u$ with respect to $v$,which is $\frac{du}{dv}$. Using the chain rule,$\frac{du}{dv} = \frac{du/dx}{dv/dx}$. First,differentiate $u$ with respect to $x$: $\frac{du}{dx} = \frac{d}{dx}(x^3) = 3x^2$. Next,differentiate $v$ with respect to $x$: $\frac{dv}{dx} = \frac{d}{dx}(x^2) = 2x$. Therefore,$\frac{du}{dv} = \frac{3x^2}{2x} = \frac{3}{2}x$.

The differential coefficient of ${x^3}$ with respect to ${x^2}$ is:

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