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Beliebt Rechnen >

(\partial)/(\partial x)(cos(x^2)sin(zy))

Lösung

\frac{\partial}{\partial x} (cos (x^{2}) \cdot sin (z \cdot y))

Lösung

- 2 x sin (zy) sin (x^{2})

Schritte zur Lösung

\frac{\partial}{\partial x} (cos (x^{2}) sin (zy))

Behandle

z, y

als Konstanten

Entferne die Konstante:

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

= sin (zy) \frac{\partial}{\partial x} (cos (x^{2}))

Wende die Kettenregel an:

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

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

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

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

Vereinfache

= - 2 x sin (zy) sin (x^{2})

Beliebte Beispiele

(\partial)/(\partial x)(sqrt(17-2x^2-y^2))

\frac{\partial}{\partial x} (17 - 2 x^{2} - y^{2})

(\partial)/(\partial x)(3x^2y^2-4)

\frac{\partial}{\partial x} (3 x^{2} y^{2} - 4)

derivative x^3+4x

d er i v a t i v e x^{3} + 4 x

derivative of \sqrt[5]{x^2}

\frac{d}{d x} (5 x^{2})

derivative (6x+x^2)/((3+x)^2)

d er i v a t i v e \frac{6 x + x ^{2}}{( 3 + x ) ^{2}}