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

The derivative of 1/x+1/(x^3)-4/(sqrt(x)) is (-x^{7/2}-3x^{3/2}+2x^4)/(x^{11/2)}

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

The first derivative of 1/x+1/(x^3)-4/(sqrt(x)) is (-x^{7/2}-3x^{3/2}+2x^4)/(x^{11/2)}

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derivative of

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

\frac{- x ^{\frac{7}{2}} - 3 x ^{\frac{3}{2}} + 2 x ^{4}}{x ^{\frac{11}{2}}}

Solution steps

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

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

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

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

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

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

Simplify

- \frac{1}{x ^{2}} - \frac{3}{x ^{4}} - (- \frac{2}{x ^{\frac{3}{2}}}) : \frac{- x ^{\frac{7}{2}} - 3 x ^{\frac{3}{2}} + 2 x ^{4}}{x ^{\frac{11}{2}}}

= \frac{- x ^{\frac{7}{2}} - 3 x ^{\frac{3}{2}} + 2 x ^{4}}{x ^{\frac{11}{2}}}

\frac{d}{d x} (\frac{x}{x ^{2} - x + 25})

\frac{d}{d t} (t^{n} e^{a t})

\int (3 x + 4)^{2} d x

x \to 2 lim (\frac{∣ x - 2 ∣}{2 - x})

x \to 0 lim (- 2 x^{2})

What is the derivative of 1/x+1/(x^3)-4/(sqrt(x)) ?
The derivative of 1/x+1/(x^3)-4/(sqrt(x)) is (-x^{7/2}-3x^{3/2}+2x^4)/(x^{11/2)}
What is the first derivative of 1/x+1/(x^3)-4/(sqrt(x)) ?
The first derivative of 1/x+1/(x^3)-4/(sqrt(x)) is (-x^{7/2}-3x^{3/2}+2x^4)/(x^{11/2)}