(\partial)/(\partial x)(arcsin(y/((x^2+y^2)^{1/2)}))

Lösung

\frac{\partial}{\partial x} (arcsin (\frac{y}{( x ^{2} + y ^{2} ) ^{\frac{1}{2}}}))

- \frac{y}{x ^{2} + y ^{2}}

Schritte zur Lösung

\frac{\partial}{\partial x} (arcsin (\frac{y}{( x ^{2} + y ^{2} ) ^{\frac{1}{2}}}))

Behandle

y

als Konstante

Wende die Kettenregel an:

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

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

\frac{\partial}{\partial x} (\frac{y}{( x ^{2} + y ^{2} ) ^{\frac{1}{2}}}) = - \frac{y x}{( x ^{2} + y ^{2} ) ^{\frac{3}{2}}}

= \frac{1}{1 - ( \frac{y}{( x ^{2} + y ^{2} ) ^{\frac{1}{2}}} ) ^{2}} (- \frac{y x}{( x ^{2} + y ^{2} ) ^{\frac{3}{2}}})

Vereinfache

\frac{1}{1 - ( \frac{y}{( x ^{2} + y ^{2} ) ^{\frac{1}{2}}} ) ^{2}} (- \frac{y x}{( x ^{2} + y ^{2} ) ^{\frac{3}{2}}}) : - \frac{y}{x ^{2} + y ^{2}}

= - \frac{y}{x ^{2} + y ^{2}}

\int tan (x) - 2 sin (x) d x

\frac{d}{d x} (\frac{300}{x})

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

s im pl i f y f (x) g (x) h (x)

d er i v a t i v e \frac{( 3 t )}{t - 3}