# arrow_back Differentiate $k(t)=\frac{(t+2)^{3}}{\sqrt{t}}$ with respect to $t$

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Differentiate $k(t)=\dfrac{(t+2)^{3}}{\sqrt{t}}$ with respect to $t$

\begin{aligned} k(t) &=\frac{(t+2)^{3}}{\sqrt{t}} \\ &=\frac{(t+2)\left(t^{2}+4 t+4\right)}{\sqrt{t}} \\ &=\frac{t^{3}+6 t^{2}+12 t+8}{t^{\frac{1}{2}}} \\ &=t^{-\frac{1}{2}}\left(t^{3}+6 t^{2}+12 t+8\right) \\ &=t^{\frac{5}{2}}+6 t^{\frac{3}{2}}+12 t^{\frac{1}{2}}+8 t^{-\frac{1}{2}} \end{aligned}
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