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Beliebt Rechnen >

derivative of x^{1/2}*csc(xsin(x))

Lösung

\frac{d}{d x} (x^{\frac{1}{2}} \cdot csc (x) sin (x))

Lösung

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

Schritte zur Lösung

\frac{d}{d x} (x^{\frac{1}{2}} csc (x) sin (x))

Vereinfache

x^{\frac{1}{2}} csc (x) sin (x) : x^{\frac{1}{2}}

= \frac{d}{d 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{1}{2}}}

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

Graph

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