(\partial)/(\partial x)(sqrt(1-(x^2+y^2)))

Lösung

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

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

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

\int x^{3} x^{2} + 3 d x

d er i v a t i v e f (x) = 5 e^{4 x}

x \frac{d y}{d x} + 2 y = - 3 e^{x}

\int 2 x^{- 4} d x

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