Dillard

2021-05-11

Find derivatives for the functions. Assume a, b, c, and k are constants.
$f\left(t\right)=2t{e}^{t}-\frac{1}{\sqrt{t}}$

krolaniaN

${f}^{\prime }\left(t\right)={\left(2t{e}^{t}-{t}^{-\frac{1}{2}}\right)}^{\prime }$
$={\left(2t{e}^{t}\right)}^{\prime }-{\left({t}^{\frac{1}{2}}\right)}^{\prime }$
$=2t{\left({e}^{t}\right)}^{\prime }+{\left(2t\right)}^{\prime }{e}^{t}+\frac{1}{2}{t}^{\frac{3}{2}}$
$=2\left(t+1\right){e}^{t}+\frac{1}{2\sqrt{{t}^{3}}}$

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