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

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

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

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

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derivative of

- \frac{1}{x} - \frac{1}{x ^{2}} + \frac{1}{x ^{3}}

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

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

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

Simplify

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

\frac{s + 1}{s ( s + 2 ) ( s + 4 )}

\frac{1}{s ^{2} ( s - 3 ) ^{2}}

\int \frac{1}{t - 2} d t

\int \frac{3 x ^{3}}{4 - x ^{2}} d x

\int \frac{1}{x ^{n}} d x

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