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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\frac{d}{d x} (\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}}

x \to 0 lim (\frac{x - 1}{x ^{3} + x})

y = sin (5 x) + cos (6 x)

\int \frac{x ^{2}}{x} d x

\frac{d}{d x} (ln (2 x) d x)

y = - \frac{5}{9} x + 5, (4, 11)

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)