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
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)=

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,
$$\displaystyle{g}'{\left({y}\right)}={\left({2}{y}+{y}^{{{2}}}\right)}+{\left({y}-{4}\right)}{\left({2}+{2}{y}\right)}$$