Question

Calculate the derivatives of all orders: f'(x),f''(x),f'''(x),f^{4}(x),...,f^{4}(x),...,f^{n}(x),...,f(x)=(-2x+1)^{3}

Derivatives
ANSWERED
asked 2021-05-21

Calculate the derivatives of all orders: \(f'(x),f''(x),f'''(x),f^{4}(x),...,f^{4}(x),...,f^{n}(x),...,f(x)=(-2x+1)^{3}\)

Answers (1)

2021-05-22
\(\displaystyle{f}'{\left({x}\right)}=-{6}{\left(-{2}{x}+{1}\right)}^{{{2}}}\)
\(\displaystyle{f}{''}{\left({x}\right)}={24}{\left(-{2}{x}+{1}\right)}\)
\(\displaystyle{f}{'''}{\left({x}\right)}=-{48}\)
\(\displaystyle{{f}^{{{4}}}{\left({x}\right)}}=\ldots={{f}^{{{n}}}{\left({x}\right)}}={0}\)
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