(\partial)/(\partial x)(4e^{yz}cos(xyz))

Lösung

\frac{\partial}{\partial x} (4 e^{yz} cos (x yz))

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

Schritte zur Lösung

\frac{\partial}{\partial x} (4 e^{yz} cos (x yz))

Behandle

y, z

als Konstanten

Entferne die Konstante:

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

= 4 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

= 4 e^{yz} (- sin (x yz) yz)

Vereinfache

= - 4 e^{yz} yz sin (yz x)

x \to 7 lim (\frac{- 2}{7 - x})

t an g e n t y = \frac{6 x}{x + 2}, (4, 4)

\int \frac{( x - 2 )}{x ^{2} - 7 x + 12} d x

\int \frac{1}{x lo g _{10} ( x )} d x

\int (- 18 x^{2} - 10) csc^{2} (3 x^{3} + 5 x) d x