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

9 views
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}
by Platinum
(106,910 points)

## Related questions

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
Differentiate $g(t)=4(t+1)^{2}(t-3)$ with respect to $t$
Differentiate $g(t)=4(t+1)^{2}(t-3)$ with respect to $t$Differentiate &nbsp;$g(t)=4(t+1)^{2}(t-3)$ with respect to $t$ ...
close

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
Differentiate $\frac{5 x^{3}+x^{2}}{x}, x \neq 0$ with respect to $x$
Differentiate $\frac{5 x^{3}+x^{2}}{x}, x \neq 0$ with respect to $x$Differentiate $\frac{5 x^{3}+x^{2}}{x}, x \neq 0$ with respect to $x$ A. $10 x+1$ B. $10 x+2$ C. $x(15 x+1)$ D. $x(15 x+2)$ ...
close

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
Differentiate the function $y=3 x^{5}$
Differentiate the function $y=3 x^{5}$Differentiate the function $y=3 x^{5}$ ...
close

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
Differentiate $y=\dfrac{3+x^2}{3-x^2}$ with respect to $x$
Differentiate $y=\dfrac{3+x^2}{3-x^2}$ with respect to $x$Differentiate $y=\dfrac{3+x^2}{3-x^2}$ with respect to $x$ ...
close

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
Differentiate $y=(\sec x)^{\frac{1}{4}}$ with respect to $x$
Differentiate $y=(\sec x)^{\frac{1}{4}}$ with respect to $x$Differentiate $y=(\sec x)^{\frac{1}{4}}$ with respect to $x$ ...
close

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
Differentiate $y=(x^2-3x)^4\cdot\cos x$ with respect to $x$
Differentiate $y=(x^2-3x)^4\cdot\cos x$ with respect to $x$Differentiate $y=(x^2-3x)^4\cdot\cos x$ with respect to $x$ ...
Differentiate $y=\ln{(3x^{2} e^{\tan{x}})}$ with respect to $x$
Differentiate $y=\ln{(3x^{2} e^{\tan{x}})}$ with respect to $x$Differentiate $y=\ln{(3x^{2} e^{\tan{x}})}$ with respect to $x$ ...