What is the derivative of 1/(x*sqrt(x)) ?

The derivative of 1/(x*sqrt(x)) is -3/(2x^{5/2)}

What is the first derivative of 1/(x*sqrt(x)) ?

The first derivative of 1/(x*sqrt(x)) is -3/(2x^{5/2)}

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\frac{d}{d x} (\frac{1}{x \cdot x})

- \frac{3}{2 x ^{\frac{5}{2}}}

Solution steps

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

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the chain rule:

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

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

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

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

Simplify

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

= - \frac{3}{2 x ^{\frac{5}{2}}}

What is the derivative of 1/(x*sqrt(x)) ?
The derivative of 1/(x*sqrt(x)) is -3/(2x^{5/2)}
What is the first derivative of 1/(x*sqrt(x)) ?
The first derivative of 1/(x*sqrt(x)) is -3/(2x^{5/2)}