Question

Find the derivatives: show several steps For g(x)=e^{7x}, find g^{(17)}(x)

Derivatives
ANSWERED
asked 2021-03-01
Find the derivatives: show several steps
For \(\displaystyle{g{{\left({x}\right)}}}={e}^{{{7}{x}}}\), find \(\displaystyle{{g}^{{{\left({17}\right)}}}{\left({x}\right)}}\)

Answers (1)

2021-03-03
Step 1
Given that,
\(\displaystyle{g{{\left({x}\right)}}}={e}^{{{7}{x}}}\)
find \(\displaystyle{{g}^{{{\left({17}\right)}}}{\left({x}\right)}}\)
Step 2
\(\displaystyle{\frac{{{d}}}{{{\left.{d}{x}\right.}}}}{g{{\left({x}\right)}}}={\frac{{{d}}}{{{\left.{d}{x}\right.}}}}{\left({e}^{{{7}{x}}}\right)}={7}{e}^{{{7}{x}}}\)
\(\displaystyle\Rightarrow{\frac{{{d}^{{{2}}}}}{{{\left.{d}{x}\right.}^{{{2}}}}}}{g{{\left({x}\right)}}}={7}^{{{2}}}{e}^{{{7}{x}}}\)
similarly, \(\displaystyle{\frac{{{d}^{{{17}}}}}{{{\left.{d}{x}\right.}^{{{17}}}}}}{g{{\left({x}\right)}}}={{g}^{{{\left({17}\right)}}}{\left({x}\right)}}={7}^{{{17}}}{e}^{{{17}{x}}}\)
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