(\partial)/(\partial x)(sqrt(9-x^2-y^2))

Lösung

\frac{\partial}{\partial x} (9 - x^{2} - y^{2})

- \frac{x}{9 - x ^{2} - y ^{2}}

Schritte zur Lösung

\frac{\partial}{\partial x} (9 - x^{2} - y^{2})

Behandle

y

als Konstante

Wende die Kettenregel an:

\frac{1}{2 9 - x ^{2} - y ^{2}} \frac{\partial}{\partial x} (9 - x^{2} - y^{2})

= \frac{1}{2 9 - x ^{2} - y ^{2}} \frac{\partial}{\partial x} (9 - x^{2} - y^{2})

\frac{\partial}{\partial x} (9 - x^{2} - y^{2}) = - 2 x

= \frac{1}{2 9 - x ^{2} - y ^{2}} (- 2 x)

Vereinfache

\frac{1}{2 9 - x ^{2} - y ^{2}} (- 2 x) : - \frac{x}{9 - x ^{2} - y ^{2}}

= - \frac{x}{9 - x ^{2} - y ^{2}}

\frac{d}{d x} (ln (\frac{x ^{2}}{2 x ^{2} + 3 x + 2}))

t an g e n t y = \frac{π}{( 2 x ) ^{4}}

\int \frac{2}{x ^{2} + 9} d x

\frac{x d y}{d x} = 2 y

im pl i c i t \frac{d y}{d x}, y = 2 9^{x}