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

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

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

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

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

\frac{5}{x ^{6}} + \frac{3}{x ^{4}} - \frac{1}{x ^{2}}

Solution steps

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

Apply the Sum/Difference Rule:

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

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

\frac{d}{d x} (\frac{1}{x ^{5}}) = - \frac{5}{x ^{6}}

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

\frac{d}{d x} (\frac{1}{x}) = - \frac{1}{x ^{2}}

= - (- \frac{5}{x ^{6}}) - (- \frac{3}{x ^{4}}) - \frac{1}{x ^{2}}

Simplify

= \frac{5}{x ^{6}} + \frac{3}{x ^{4}} - \frac{1}{x ^{2}}

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\frac{d}{d x} (- 5 sin (5 x))

\int \frac{1}{u 1 + u ^{2}} d u

\frac{d}{d x} (7 sin (337 x + \frac{7 π}{18}))

\int_{0}^{2 π} 36 + \frac{9}{4} t d t

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