(\partial)/(\partial y)(9e^{yz}cos(xyz))

Lösung

\frac{\partial}{\partial y} (9 e^{yz} cos (x yz))

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

Schritte zur Lösung

\frac{\partial}{\partial y} (9 e^{yz} cos (x yz))

Behandle

z, x

als Konstanten

Entferne die Konstante:

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

= 9 \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)

= 9 (\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

= 9 (e^{yz} z cos (x yz) + (- sin (x yz) z x) e^{yz})

Vereinfache

= 9 (e^{yz} z cos (yz x) - e^{yz} z x sin (yz x))

\int \frac{2 x}{y ^{2}} d x

d er i v a t i v e sin (x cos (x))

\frac{d}{d x} (x^{2} e^{6 x})

\int_{3}^{7} k^{2} + 2 k - 1

\frac{d}{d x} (- 5 e^{4 x})