(\partial)/(\partial x)(5e^{yz}cos(xyz))

Lösung

\frac{\partial}{\partial x} (5 e^{yz} cos (x yz))

- 5 e^{yz} yz sin (yz x)

Schritte zur Lösung

\frac{\partial}{\partial x} (5 e^{yz} cos (x yz))

Behandle

y, z

als Konstanten

Entferne die Konstante:

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

= 5 e^{yz} \frac{\partial}{\partial x} (cos (x yz))

Wende die Kettenregel an:

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

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

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

= 5 e^{yz} (- sin (x yz) yz)

Vereinfache

= - 5 e^{yz} yz sin (yz x)

a re a x^{2} - 8 x + 15, 0

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

t an g e n t f (x) = 6 x^{2} - 4 x + 4, (1, 6)

d er i v a t i v e y = \frac{3}{e ^{x} + e ^{- x}}

\frac{d}{d x} (3 x, - 2 y, x - y)