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Beliebt Rechnen >

(\partial)/(\partial x)(ycos(x^2+y^2))

Lösung

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

Lösung

- 2 y x sin (x^{2} + y^{2})

Schritte zur Lösung

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

Behandle

y

als Konstante

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende die Kettenregel an:

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

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

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

= y (- sin (x^{2} + y^{2}) \cdot 2 x)

Vereinfache

= - 2 y x sin (x^{2} + y^{2})

Beliebte Beispiele

derivative of (-1/(1-x))

\frac{d}{d x} (\frac{- 1}{1 - x})

derivative of x/(1+sqrt(1-x^2))

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

integral of (1100x)/(x^2+80)

\int \frac{1100 x}{x ^{2} + 80} d x

tangent f(x)=sqrt(x),(64,8)

t an g e n t f (x) = x, (64, 8)

(\partial)/(\partial x)(cos(x-y))

\frac{\partial}{\partial x} (cos (x - y))