If y = t^{4/3} - 3t^{-2/3},then frac{dy}{dt} | vedclass

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(D) Given $y = t^{4/3} - 3t^{-2/3}$.Applying the power rule $\frac{d}{dt}(t^n) = nt^{n-1}$:$\frac{dy}{dt} = \frac{4}{3}t^{(4/3 - 1)} - 3 	imes (-2/3)

Vedclass · Accepted Answer

$\frac{2(2t^2 + 3)}{3t^{5/3}}$

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(D) Given $y = t^{4/3} - 3t^{-2/3}$.Applying the power rule $\frac{d}{dt}(t^n) = nt^{n-1}$:$\frac{dy}{dt} = \frac{4}{3}t^{(4/3 - 1)} - 3 	imes (-2/3)t^{(-2/3 - 1)}$$\frac{dy}{dt} = \frac{4}{3}t^{1/3} + 2t^{-5/3}$To simplify,find a common denominator of $3t^{5/3}$:$\frac{dy}{dt} = \frac{4}{3}t^{1/3} 	imes \frac{t^{5/3}}{t^{5/3}} + 2t^{-5/3} = \frac{4t^{6/3}}{3t^{5/3}} + \frac{6}{3t^{5/3}}$$\frac{dy}{dt} = \frac{4t^2 + 6}{3t^{5/3}} = \frac{2(2t^2 + 3)}{3t^{5/3}}$.

If $y = t^{4/3} - 3t^{-2/3}$,then $\frac{dy}{dt} = $

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