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Beliebt Rechnen >

(\partial)/(\partial x)(sqrt(3-x^2-y^2))

Lösung

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

Lösung

- \frac{x}{3 - x ^{2} - y ^{2}}

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

= - \frac{x}{3 - x ^{2} - y ^{2}}

Beliebte Beispiele

derivative of x*sqrt(x^2-1)

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

derivative of 1/(log_{10(x)})

\frac{d}{d x} (\frac{1}{lo g _{10} ( x )})

(\partial)/(\partial y)(4x^3y^3-1)

\frac{\partial}{\partial y} (4 x^{3} y^{3} - 1)

integral of (4+x+x^2)/(sqrt(x))

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

y^'=-y/(100),y(0)=80

y^{^{'}} = - \frac{y}{100}, y (0) = 80