Question

Consider the following. f(x)=9x^{4}-7x^{3} Find the following derivatives. f'(x)= f''(x)= f'''(x)=

Derivatives
ANSWERED
asked 2021-06-06
Consider the following.
\(\displaystyle{f{{\left({x}\right)}}}={9}{x}^{{{4}}}-{7}{x}^{{{3}}}\)
Find the following derivatives.
f'(x)=
f''(x)=
f'''(x)=

Answers (1)

2021-06-07
Step 1
By using the formula
\(\displaystyle{f{{\left({x}\right)}}}={x}^{{{n}}}\)
Then derivative of above function
\(\displaystyle{f}'{\left({x}\right)}={n}{x}^{{{n}-{1}}}\)
Step 2
\(\displaystyle{f{{\left({x}\right)}}}={9}{x}^{{{4}}}-{7}{x}^{{{3}}}\)
\(\displaystyle{f}'{\left({x}\right)}={9}\times{4}{x}^{{{4}-{1}}}-{7}\times{3}{x}^{{{3}-{1}}}\)
\(\displaystyle={36}{x}^{{{3}}}-{21}{x}^{{{2}}}\)
\(\displaystyle{f}{''}{\left({x}\right)}={108}{x}^{{{2}}}-{42}{x}\)
\(\displaystyle{f}{'''}{\left({x}\right)}={216}{x}-{42}\)
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