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Beliebt Rechnen >

(\partial)/(\partial x)(1/(sqrt(x)))

Lösung

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

Lösung

- \frac{1}{2 x ^{\frac{3}{2}}}

Schritte zur Lösung

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

Wende Exponentenregel an:

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

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

Wende die Potenzregel an:

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

= - \frac{1}{2} x^{- \frac{1}{2} - 1}

Vereinfache

- \frac{1}{2} x^{- \frac{1}{2} - 1} : - \frac{1}{2 x ^{\frac{3}{2}}}

= - \frac{1}{2 x ^{\frac{3}{2}}}

Beliebte Beispiele

integral of-e^{4x}+4x^5

\int - e^{4 x} + 4 x^{5} d x

tangent f(x)=sqrt(x),\at x=36

t an g e n t f (x) = x, at x = 36

derivative f(x)=4x^3+9

d er i v a t i v e f (x) = 4 x^{3} + 9

(- x^{- 2})^{^{'}}

(x^2+2x-1)y^'-(x+1)y=x-1

(x^{2} + 2 x - 1) y^{^{'}} - (x + 1) y = x - 1