Question

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

Derivatives
ANSWERED
asked 2021-05-11
Use the rules for derivatives to find the derivative of function defined as follows.
\(\displaystyle{q}={\left({e}^{{{2}{p}+{1}}}-{2}\right)}^{{{4}}}\)

Answers (1)

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
\(\displaystyle{q}={\left({e}^{{{2}{p}+{1}}}-{2}\right)}^{{{4}}}\)
\(\displaystyle{\frac{{{d}{q}}}{{{d}{p}}}}={4}{\left({e}^{{{2}{p}+{1}}}-{2}\right)}^{{{3}}}\cdot{e}^{{{2}{p}+{1}}}\cdot{2}\)
\(\displaystyle{\frac{{{d}{q}}}{{{d}{p}}}}={8}{\left({e}^{{{2}{p}+{1}}}-{2}\right)}^{{{3}}}\cdot{e}^{{{2}{p}+{1}}}\)
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