Question

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

Derivatives
ANSWERED
asked 2021-06-16
Find derivatives for the functions. Assume a, b, c, and k are constants.
\(\displaystyle{y}={\frac{{{x}^{{{2}}}+{2}}}{{{3}}}}^{{{2}}}\)

Answers (1)

2021-06-17
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
\(\displaystyle={\frac{{{4}{x}{\left({x}^{{{2}}}+{2}\right)}}}{{{9}}}}\)
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