derivative of arcsin(sqrt(2x))

Lösung

\frac{d}{d x} (arcsin (2 x))

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

Schritte zur Lösung

\frac{d}{d x} (arcsin (2 x))

Vereinfache

arcsin (2 x) : arcsin (2 x)

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

\frac{\partial}{\partial x} (y ln (x))

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\frac{\partial}{\partial x} (x^{2} y + x y^{2} + 20)

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\frac{d}{d y} (3 cos (3 x) (x - y) + sin (3 x))