What is the derivative of 5/x-2/(x^3+1/(x^4)) ?

The derivative of 5/x-2/(x^3+1/(x^4)) is -5/(x^2)+6/(x^4)-4/(x^5)

What is the first derivative of 5/x-2/(x^3+1/(x^4)) ?

The first derivative of 5/x-2/(x^3+1/(x^4)) is -5/(x^2)+6/(x^4)-4/(x^5)

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\frac{d}{d x} (\frac{5}{x} - \frac{2}{x ^{3}} + \frac{1}{x ^{4}})

- \frac{5}{x ^{2}} + \frac{6}{x ^{4}} - \frac{4}{x ^{5}}

Solution steps

\frac{d}{d x} (\frac{5}{x} - \frac{2}{x ^{3}} + \frac{1}{x ^{4}})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (\frac{5}{x}) - \frac{d}{d x} (\frac{2}{x ^{3}}) + \frac{d}{d x} (\frac{1}{x ^{4}})

\frac{d}{d x} (\frac{5}{x}) = - \frac{5}{x ^{2}}

\frac{d}{d x} (\frac{2}{x ^{3}}) = - \frac{6}{x ^{4}}

\frac{d}{d x} (\frac{1}{x ^{4}}) = - \frac{4}{x ^{5}}

= - \frac{5}{x ^{2}} - (- \frac{6}{x ^{4}}) - \frac{4}{x ^{5}}

Simplify

= - \frac{5}{x ^{2}} + \frac{6}{x ^{4}} - \frac{4}{x ^{5}}

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What is the derivative of 5/x-2/(x^3+1/(x^4)) ?
The derivative of 5/x-2/(x^3+1/(x^4)) is -5/(x^2)+6/(x^4)-4/(x^5)
What is the first derivative of 5/x-2/(x^3+1/(x^4)) ?
The first derivative of 5/x-2/(x^3+1/(x^4)) is -5/(x^2)+6/(x^4)-4/(x^5)