Question

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

Derivatives
ANSWERED
asked 2021-06-26
Calculate the derivatives of all orders: \(\displaystyle{f}′{\left({x}\right)},{f}{''}{\left({x}\right)},{f}{'''}{\left({x}\right)},{{f}^{{{4}}}{\left({x}\right)}},\ldots,{{f}^{{{n}}}{\left({x}\right)}},\ldots{f{{\left({x}\right)}}}−{4}{x}^{{{2}}}−{x}+{1}\)

Answers (1)

2021-06-27
Let's compute the first derivative:
f'(x)=8x-z
Let's now compute the second derivative
f''(x)=8
Let's compute the third derivative:
f'''(x)=0
The order derivatives are all zero:
\(\displaystyle{{f}^{{{4}}}{\left({x}\right)}}=\ldots={{f}^{{{n}}}{\left({x}\right)}}={0}\)
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