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Beliebt Rechnen >

(\partial)/(\partial z)(cos(xy)+sin(yz))

Lösung

\frac{\partial}{\partial z} (cos (x y) + sin (yz))

Lösung

y cos (yz)

Schritte zur Lösung

\frac{\partial}{\partial z} (cos (x y) + sin (yz))

Behandle

x, y

als Konstanten

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial z} (cos (x y)) + \frac{\partial}{\partial z} (sin (yz))

\frac{\partial}{\partial z} (cos (x y)) = 0

\frac{\partial}{\partial z} (sin (yz)) = cos (yz) y

= 0 + cos (yz) y

Vereinfache

= y cos (yz)

Beliebte Beispiele

integral of sin^3(x)cos^2(x)

\int sin^{3} (x) cos^{2} (x) d x

integral from 1 to e^2 of (ln^5(x^2))/x

\int_{1}^{e^{2}} \frac{ln ^{5} ( x ^{2} )}{x} d x

derivative f(x)=(4x-5)(3x^3-x^2+1)

d er i v a t i v e f (x) = (4 x - 5) (3 x^{3} - x^{2} + 1)

integral of (x-3)/(x^2-1)

\int \frac{x - 3}{x ^{2} - 1} d x

derivative sqrt(x^3)

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