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Beliebt Rechnen >

(\partial)/(\partial x)(cos(xy)-1-sin(y))

Lösung

\frac{\partial}{\partial x} (cos (x y) - 1 - sin (y))

Lösung

- y sin (x y)

Schritte zur Lösung

\frac{\partial}{\partial x} (cos (x y) - 1 - sin (y))

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{\partial}{\partial x} (cos (x y)) - \frac{\partial}{\partial x} (1) - \frac{\partial}{\partial x} (sin (y))

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

\frac{\partial}{\partial x} (1) = 0

\frac{\partial}{\partial x} (sin (y)) = 0

= - sin (x y) y - 0 - 0

Vereinfache

= - y sin (x y)

Beliebte Beispiele

derivative of x^2+6x-16

\frac{d}{d x} (x^{2} + 6 x - 16)

derivative 6/((1-x)^3)

d er i v a t i v e \frac{6}{( 1 - x ) ^{3}}

limit as k approaches infinity of (-1)^k

k \to \infty lim ((- 1)^{k})

limit as x approaches infinity of 7x^2

x \to \infty lim (7 x^{2})

(\partial)/(\partial y)(x*y)

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