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Beliebt Rechnen >

(\partial)/(\partial y)(8e^{yz}cos(xyz))

Lösung

\frac{\partial}{\partial y} (8 e^{yz} cos (x yz))

Lösung

8 (e^{yz} z cos (yz x) - e^{yz} z x sin (yz x))

Schritte zur Lösung

\frac{\partial}{\partial y} (8 e^{yz} cos (x yz))

Behandle

z, x

als Konstanten

Entferne die Konstante:

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

= 8 \frac{\partial}{\partial y} (e^{yz} cos (x yz))

Wende die Produktregel an:

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

f = e^{yz}, g = cos (x yz)

= 8 (\frac{\partial}{\partial y} (e^{yz}) cos (x yz) + \frac{\partial}{\partial y} (cos (x yz)) e^{yz})

\frac{\partial}{\partial y} (e^{yz}) = e^{yz} z

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

= 8 (e^{yz} z cos (x yz) + (- sin (x yz) z x) e^{yz})

Vereinfache

= 8 (e^{yz} z cos (yz x) - e^{yz} z x sin (yz x))

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steigung (4.8)(2.12)

s l o p e (4.8) (2.12)

derivative of sqrt(xe^{2x)}

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

integral of sin^2(pi/4+t/2)

\int sin^{2} (\frac{π}{4} + \frac{t}{2}) d t

limit as x approaches-7 of x^2-49

x \to - 7 lim (x^{2} - 49)

derivative 1/(t^2+5t-1)

d er i v a t i v e \frac{1}{t ^{2} + 5 t - 1}