(\partial)/(\partial x)(sin(xe^{x^2y}))

Lösung

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

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

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Kettenregel an:

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

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

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

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

\int (sin^{3} (2 t)) cos (2 t) d t

(3 x^{2})^{^{'}}

\int \frac{x ^{2}}{x ^{6} + 1} d x

d er i v a t i v e f (x) = ln (x + x^{2} + 1)

\int (7 + e) d x