Question

x × (60-x)^3 differentiate​

Answer 1

SOLUTION

TO DETERMINE

The differentiate

$\displaystyle \sf{x {(60 -x)}^{3} }$

EVALUATION

Here the given expression is

$\displaystyle \sf{y = x {(60 -x)}^{3} }$

Differentiating both sides with respect to x we get

$\displaystyle \sf{ \frac{dy}{dx} = \frac{d}{dx} \bigg[x {(60 -x)}^{3}\bigg] }$

$\displaystyle \sf{ \implies \frac{dy}{dx} = x. \frac{d}{dx} \bigg[ {(60 -x)}^{3}\bigg] + {(60 -x)}^{3} \frac{d}{dx}(x) }$

$\displaystyle \sf{ \implies \frac{dy}{dx} = - 3 x. {(60 -x)}^{2}+ {(60 -x)}^{3} }$

$\displaystyle \sf{ \implies \frac{dy}{dx} = {(60 -x)}^{2} {( - 3x + 60 -x)}^{} }$

$\displaystyle \sf{ \implies \frac{dy}{dx} = {(60 -x)}^{2} {( 60 -4x)}^{} }$

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