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Beliebt Rechnen >

(\partial)/(\partial y)(xycos(yz))

Lösung

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

Lösung

x (cos (yz) - yz sin (yz))

Schritte zur Lösung

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

Behandle

x, z

als Konstanten

Entferne die Konstante:

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

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

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = y, g = cos (yz)

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

\frac{\partial}{\partial y} (y) = 1

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

= x (1 \cdot cos (yz) + (- sin (yz) z) y)

Vereinfache

= x (cos (yz) - yz sin (yz))

Beliebte Beispiele

(dy}{dx}=\frac{x^2+3)/y

\frac{d y}{d x} = \frac{x ^{2} + 3}{y}

derivative f(x)=ln(sqrt(x^2-4))

d er i v a t i v e f (x) = ln (x^{2} - 4)

integral of (x-1)e^{-x}

\int (x - 1) e^{- x} d x

(d^2)/(dx^2)(6x+17)

\frac{d ^{2}}{d x ^{2}} (6 x + 17)

integral of sin^2(x)*cos^4(x)

\int sin^{2} (x) \cdot cos^{4} (x) d x