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

Lösung

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

- 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} (cos (y e^{x y}) sin (x))

Behandle

y

als Konstante

Wende die Produktregel an:

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

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

= \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)

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

Vereinfache

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

\int \frac{( a ^{2} - x ^{2} ) ^{\frac{3}{2}}}{x ^{4}} d x

x \to 0 lim (\frac{sin ( 16 x )}{3 x})

\int 3^{2 x} d x

\frac{d}{d x} (2, x)

x \to 0 lim (\frac{x - 7}{3 x + 4})