(\partial)/(\partial x)(sin(x)e^{yx^2}x)

Lösung

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

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

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Produktregel an:

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

f = sin (x), g = e^{y x^{2}} x

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

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

\frac{\partial}{\partial x} (e^{y x^{2}} x) = 2 y e^{y x^{2}} x^{2} + e^{y x^{2}}

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

\int \frac{z}{1 + z ^{2}} d z

\int e^{x^{2} - 2 x} d x

\frac{d}{d x} (x^{\frac{1}{2}} \cdot csc (x) sin (x))

2 y^{^{'}} - 6 x^{2} = 0

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