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Popular >

derivative of (ln|x|^e+x/(11))

Solution

\frac{d}{d x} ((ln ∣ x ∣)^{e} + \frac{x}{11})

Solution

\frac{e ln ∣ x ∣ ^{e - 1}}{x} + \frac{1}{11}

Solution steps

\frac{d}{d x} ((ln ∣ x ∣)^{e} + \frac{x}{11})

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} ((ln ∣ x ∣)^{e}) + \frac{d}{d x} (\frac{x}{11})

\frac{d}{d x} ((ln ∣ x ∣)^{e}) = \frac{e ln ∣ x ∣ ^{e - 1}}{x}

\frac{d}{d x} (\frac{x}{11}) = \frac{1}{11}

= \frac{e ln ∣ x ∣ ^{e - 1}}{x} + \frac{1}{11}

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Frequently Asked Questions (FAQ)

What is the derivative of (ln|x|^e+x/(11)) ?
The derivative of (ln|x|^e+x/(11)) is (eln|x|^{e-1})/x+1/11
What is the first derivative of (ln|x|^e+x/(11)) ?
The first derivative of (ln|x|^e+x/(11)) is (eln|x|^{e-1})/x+1/11