# Using the Extended Power Rule Find the following derivatives. \frac{d}{dt}(\frac{3t^{16}-4}{t^{6}})

Using the Extended Power Rule Find the following derivatives.
$$\displaystyle{\frac{{{d}}}{{{\left.{d}{t}\right.}}}}{\left({\frac{{{3}{t}^{{{16}}}-{4}}}{{{t}^{{{6}}}}}}\right)}$$

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mhalmantus
$$\displaystyle{\frac{{{d}}}{{{\left.{d}{t}\right.}}}}{\left({\frac{{{3}{t}^{{{16}}}-{4}}}{{{t}^{{{6}}}}}}\right)}={\frac{{{d}}}{{{\left.{d}{x}\right.}}}}{\left({\frac{{{3}{t}^{{{16}}}}}{{{t}^{{{6}}}}}}-{\frac{{{4}}}{{{t}^{{{6}}}}}}\right)}$$
$$\displaystyle={\frac{{{d}}}{{{\left.{d}{x}\right.}}}}{\left({3}{t}^{{{10}}}-{4}{t}^{{-{6}}}\right)}$$
$$\displaystyle={3}{\frac{{{d}}}{{{\left.{d}{t}\right.}}}}{\left({t}^{{{10}}}\right)}-{4}{\frac{{{d}}}{{{\left.{d}{t}\right.}}}}{\left({t}^{{-{6}}}\right)}$$
$$\displaystyle={30}{t}^{{{9}}}-{24}{t}^{{-{7}}}$$
$$\displaystyle={30}{t}^{{{9}}}-{\frac{{{24}}}{{{t}^{{{7}}}}}}$$