# Use the rules for derivatives to find the derivative of function defined as follows. q=(e^{2p+1}-2)^{4}

Derivatives
Use the rules for derivatives to find the derivative of function defined as follows.
$$\displaystyle{q}={\left({e}^{{{2}{p}+{1}}}-{2}\right)}^{{{4}}}$$

2021-05-12
Step 1 Derivative
Use the rules for derivatives to find the derivative of function defined as follows.
$$\displaystyle{q}={\left({e}^{{{2}{p}+{1}}}-{2}\right)}^{{{4}}}$$
Step 2 Formulation
$$\displaystyle{\frac{{{d}}}{{{\left.{d}{x}\right.}}}}{\left({x}^{{{n}}}\right)}={n}{x}^{{{n}-{1}}}$$
$$\displaystyle{\frac{{{d}}}{{{\left.{d}{x}\right.}}}}{\left({e}^{{{x}}}\right)}={e}^{{{x}}}$$
Step 3 Solution
$$\displaystyle{q}={\left({e}^{{{2}{p}+{1}}}-{2}\right)}^{{{4}}}$$
$$\displaystyle{\frac{{{d}{q}}}{{{d}{p}}}}={4}{\left({e}^{{{2}{p}+{1}}}-{2}\right)}^{{{3}}}\cdot{e}^{{{2}{p}+{1}}}\cdot{2}$$
$$\displaystyle{\frac{{{d}{q}}}{{{d}{p}}}}={8}{\left({e}^{{{2}{p}+{1}}}-{2}\right)}^{{{3}}}\cdot{e}^{{{2}{p}+{1}}}$$