Question

Calculate the derivatives of all orders: f'(x), f''(x), f'''(x), f^{4},...,f^{n}(x),...,f(x)=e^{3x-1}

Derivatives
ANSWERED
asked 2021-05-19

Calculate the derivatives of all orders: f'(x), f''(x), f'''(x), \(\displaystyle{f}^{{{4}}},\ldots,{{f}^{{{n}}}{\left({x}\right)}},\ldots,{f{{\left({x}\right)}}}={e}^{{{3}{x}-{1}}}\)

Answers (1)

2021-05-20
\(\displaystyle{f}'{\left({x}\right)}={3}{e}^{{{3}{x}-{1}}}\)
\(\displaystyle{f}{''}{\left({x}\right)}={9}{e}^{{{3}{x}-{1}}}\)
\(\displaystyle{f}{'''}{\left({x}\right)}={27}{e}^{{{3}{x}-{1}}}\)
\(\displaystyle{{f}^{{{4}}}{\left({x}\right)}}={81}{e}^{{{3}{x}-{1}}}\)
\(\displaystyle={{f}^{{{n}}}{\left({x}\right)}}={3}^{{{n}}}{e}^{{{3}{x}-{1}}}\)
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