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Differentiate the following functions $f(x)$ with respect to $x$.

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Input all numbers as fractions or integers, not as decimals.

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If $f(x)=x^{{n}}$

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$f'(x)={n}*x^{{n-1}}={n}x^{{n-1}}$

\n

\n

If $f(x)={a}x^{{n}}$

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$f'(x)={a}*{n}*x^{{n-1}}={a}{n}x^{{n-1}}$

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coefficient

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index

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coefficient

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index

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denominator

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$f(x)=x^{\\var{n}}$

\n

$f'(x)=\\;$[[0]]

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$f(x)=x^{\\var{m}}$

\n

$\\displaystyle f'(x)=\\;$[[0]]

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$f(x)=\\var{a}x^{\\var{n}}$

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$f'(x)=\\;$[[0]]

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$f(x)=\\var{b}x^{\\var{m}}$

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$f'(x)=\\;$[[0]]

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