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

The derivative of x^2+(2x/(sqrt(x))-1/(x^2)) is (x^{5/2}+2+2x^4)/(x^{5/2)sqrt(x)}

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

The first derivative of x^2+(2x/(sqrt(x))-1/(x^2)) is (x^{5/2}+2+2x^4)/(x^{5/2)sqrt(x)}

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

\frac{x ^{\frac{5}{2}} + 2 + 2 x ^{4}}{x ^{\frac{5}{2}} x}

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

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

Simplify

2 x + \frac{1}{x} - (- \frac{2}{x ^{3}}) : \frac{x ^{\frac{5}{2}} + 2 + 2 x ^{4}}{x ^{\frac{5}{2}} x}

= \frac{x ^{\frac{5}{2}} + 2 + 2 x ^{4}}{x ^{\frac{5}{2}} x}

\int cos^{3} (\frac{x}{7}) d x

\int (x + 5) ln (x) d x

\frac{d}{d x} (e^{x} sin (e^{x}))

\frac{d}{d x} (x^{2} + x y)

\frac{d}{d t} (e^{3 c o s (t) + 2 t^{2}})

What is the derivative of x^2+(2x/(sqrt(x))-1/(x^2)) ?
The derivative of x^2+(2x/(sqrt(x))-1/(x^2)) is (x^{5/2}+2+2x^4)/(x^{5/2)sqrt(x)}
What is the first derivative of x^2+(2x/(sqrt(x))-1/(x^2)) ?
The first derivative of x^2+(2x/(sqrt(x))-1/(x^2)) is (x^{5/2}+2+2x^4)/(x^{5/2)sqrt(x)}