# Find derivatives for the functions. Assume a, b, c, and k are constants. s(t)=6 t^{-2}+3 t^{3}-4 t^{1 &#x2F; 2}

Find derivatives for the functions. Assume a, b, c, and k are constants. $$\displaystyle{s}{\left({t}\right)}={6}{t}^{{-{2}}}+{3}{t}^{{{3}}}-{4}{t}^{{{\frac{{{1}}}{{{2}}}}}}$$

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avortarF
Find derivative of given function:
$$\displaystyle{s}'{\left({t}\right)}=^{{{1}}}{\left({6}{t}^{{-{2}}}\right)}'+{\left({3}{t}^{{{3}}}\right)}'-{\left({4}{t}^{{{\frac{{{1}}}{{{2}}}}}}\right)}'$$
$$\displaystyle=^{{{2}}}{6}\dot{{-{2}{t}^{{{3}}}}}+{3}\dot{{3}}{t}^{{{2}}}-{4}\dot{{\frac{{{1}}}{{{2}}}}}{t}^{{-{\frac{{{1}}}{{{2}}}}}}$$
$$\displaystyle=-{12}{t}^{{-{3}}}+{9}{t}^{{{2}}}-{2}{t}^{{-{\frac{{{1}}}{{{2}}}}}}$$
Rules used:
(1) Derivative of sum
(2) Power rule