What is the derivative of (d^2/(dx^2)(1/x)-ln(x)) ?

The derivative of (d^2/(dx^2)(1/x)-ln(x)) is -6/(x^4)-2/(x^3)

What is the first derivative of (d^2/(dx^2)(1/x)-ln(x)) ?

The first derivative of (d^2/(dx^2)(1/x)-ln(x)) is -6/(x^4)-2/(x^3)

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

- \frac{6}{x ^{4}} - \frac{2}{x ^{3}}

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

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

What is the derivative of (d^2/(dx^2)(1/x)-ln(x)) ?
The derivative of (d^2/(dx^2)(1/x)-ln(x)) is -6/(x^4)-2/(x^3)
What is the first derivative of (d^2/(dx^2)(1/x)-ln(x)) ?
The first derivative of (d^2/(dx^2)(1/x)-ln(x)) is -6/(x^4)-2/(x^3)