(\partial)/(\partial x)(sqrt(a^2-x^2-y^2))

Lösung

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

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

Schritte zur Lösung

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

Behandle

a, y

als Konstante

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

\int \frac{e ^{x^{2}}}{x} d x

x \to 3 lim (\frac{5}{2 x - 6})

\int (5 - 3 x) e^{2 x + 3} d x

\int \frac{1}{x ( x + 1 ) ^{3}} d x

\frac{\partial ^{2}}{\partial u ( w ) \partial w} (e^{u (w) - w})