(\partial)/(\partial x)(arcsin(x/l))

Lösung

\frac{\partial}{\partial x} (arcsin (\frac{x}{l}))

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

Schritte zur Lösung

\frac{\partial}{\partial x} (arcsin (\frac{x}{l}))

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

\frac{d}{d x} (\frac{3}{5 x ^{\frac{2}{5}}})

\int \frac{2 x ^{4}}{3 x ^{2}} d x

\int (\frac{e ^{x}}{2} + x x) d x

y^{^{'}} = \frac{4 x ^{7} e ^{\frac{y}{x}} + x ^{5} y ^{2}}{x ^{6} y}

\frac{d}{d x} (\frac{sin ( x )}{ln ( x )})