# Find derivatives for the functions. Assume a, b, c, and k are constants. y=\frac{x^{2}+2}{3}^{2}

Find derivatives for the functions. Assume a, b, c, and k are constants.
$$\displaystyle{y}={\frac{{{x}^{{{2}}}+{2}}}{{{3}}}}^{{{2}}}$$

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Roosevelt Houghton
Rewtire y
$$\displaystyle{y}={\left({\frac{{{x}^{{{2}}}+{2}}}{{{3}}}}\right)}^{{{2}}}={3}^{{-{2}}}{\left({x}^{{{2}}}+{2}\right)}^{{{2}}}$$
then
$$\displaystyle{y}'={\left[{3}^{{-{2}}}{\left({x}^{{{2}}}+{2}\right)}^{{{2}}}\right]}'$$
$$\displaystyle={3}^{{-{2}}}{\left({x}^{{{2}}}+{2}\right)}'\dot{{2}}{\left({x}^{{{2}}}+{2}\right)}$$ Chain rule
$$\displaystyle={\frac{{{4}{x}{\left({x}^{{{2}}}+{2}\right)}}}{{{9}}}}$$