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Beliebt Rechnen >

(\partial)/(\partial x)(cos(xy)sin(2y))

Lösung

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

Lösung

- y sin (x y) sin (2 y)

Schritte zur Lösung

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

Behandle

y

als Konstante

Entferne die Konstante:

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

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

Wende die Kettenregel an:

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

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

\frac{\partial}{\partial x} (x y) = y

= sin (2 y) (- sin (x y) y)

Vereinfache

= - y sin (x y) sin (2 y)

Beliebte Beispiele

derivative x-2ln(x+1)

d er i v a t i v e x - 2 ln (x + 1)

y^{^{'}} + 2 y = e^{- t}

integral from 1 to 4 of pi(x-1)

\int_{1}^{4} π (x - 1) d x

derivative 2(2-3x)^2

d er i v a t i v e 2 (2 - 3 x)^{2}

integral from 0 to 1 of x^k

\int_{0}^{1} x^{k} d x