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Popular >

derivative of 1/(x*sqrt(x))

Solution

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

Solution

- \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}}}

Popular Examples

integral of 2t^3

\int 2 t^{3} d t

derivative of t/((t-2)^2)derivative of

\frac{t}{( t - 2 ) ^{2}}

5 y^{^{''}} - 4 y^{^{'}} = 0

integral of 2/(xsqrt(x^2+1))

\int \frac{2}{x x ^{2} + 1} d x

inverse oflaplace (e^{-s})/(s*(s+5)^2)inverse laplace

\frac{e ^{- s}}{s \cdot ( s + 5 ) ^{2}}

Frequently Asked Questions (FAQ)

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)}