The differential coefficient of {x^6} with re | vedclass

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Question

(B) Let $y = {x^6}$ and $z = {x^3}$.We need to find the derivative of $y$ with respect to $z$,which is $\frac{dy}{dz}$.Using the chain rule,$\frac{dy}

Vedclass · Accepted Answer

$2{x^3}$

Vedclass · Answer

(B) Let $y = {x^6}$ and $z = {x^3}$.We need to find the derivative of $y$ with respect to $z$,which is $\frac{dy}{dz}$.Using the chain rule,$\frac{dy}{dz} = \frac{dy/dx}{dz/dx}$.First,differentiate $y$ with respect to $x$: $\frac{dy}{dx} = \frac{d}{dx}({x^6}) = 6{x^5}$.Next,differentiate $z$ with respect to $x$: $\frac{dz}{dx} = \frac{d}{dx}({x^3}) = 3{x^2}$.Now,substitute these values into the formula:$\frac{dy}{dz} = \frac{6{x^5}}{3{x^2}} = 2{x^3}$.Therefore,the correct option is $B$.

The differential coefficient of ${x^6}$ with respect to ${x^3}$ is

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