Question

Use the Differentiation Formulas and Rules of Derivatives to find the derivatives of the following functions. g(y)=(y-4)(2y+y^{2}) g'(y)=

Derivatives
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asked 2021-06-06
Use the Differentiation Formulas and Rules of Derivatives to find the derivatives of the following functions.
\(\displaystyle{g{{\left({y}\right)}}}={\left({y}-{4}\right)}{\left({2}{y}+{y}^{{{2}}}\right)}\)
g'(y)=

Answers (1)

2021-06-07
Step 1
Given,
\(\displaystyle{g{{\left({y}\right)}}}={\left({y}-{4}\right)}{\left({2}{y}+{y}^{{{2}}}\right)}\)
Step 2
\(\displaystyle{g}'{\left({y}\right)}={\left({2}{y}+{y}^{{{2}}}\right)}{\frac{{{d}}}{{{\left.{d}{x}\right.}}}}{\left({y}-{4}\right)}+{\left({y}-{4}\right)}{\frac{{{d}}}{{{\left.{d}{x}\right.}}}}{\left({2}{y}+{y}^{{{2}}}\right)}\)
\(\displaystyle={\left({2}{y}+{y}^{{{2}}}\right)}{\left({1}\right)}+{\left({y}-{4}\right)}{\left({2}+{2}{y}\right)}\)
\(\displaystyle={\left({2}{y}+{y}^{{{2}}}\right)}+{\left({y}-{4}\right)}{\left({2}+{2}{y}\right)}\)
Hence,
\(\displaystyle{g}'{\left({y}\right)}={\left({2}{y}+{y}^{{{2}}}\right)}+{\left({y}-{4}\right)}{\left({2}+{2}{y}\right)}\)
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