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Beliebt Rechnen >

(\partial)/(\partial x)(9cos(ye^{xy})sin(x))

Lösung

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

Lösung

9 (- e^{y x} y^{2} sin (e^{y x} y) sin (x) + cos (e^{y x} y) cos (x))

Schritte zur Lösung

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

Behandle

y

als Konstante

Entferne die Konstante:

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

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

Wende die Produktregel an:

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

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

= 9 (\frac{\partial}{\partial x} (cos (y e^{x y})) sin (x) + \frac{\partial}{\partial x} (sin (x)) cos (y e^{x y}))

\frac{\partial}{\partial x} (cos (y e^{x y})) = - sin (y e^{x y}) y^{2} e^{y x}

\frac{\partial}{\partial x} (sin (x)) = cos (x)

= 9 ((- sin (y e^{x y}) y^{2} e^{y x}) sin (x) + cos (x) cos (y e^{x y}))

Vereinfache

= 9 (- e^{y x} y^{2} sin (e^{y x} y) sin (x) + cos (e^{y x} y) cos (x))

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fläche x^2-19,18x

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\frac{\partial}{\partial x} (1 + x \cdot ln (x y - 5))

integral of 7e^{cos(x)}sin(x)

\int 7 e^{c o s (x)} sin (x) d x

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

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