(\partial)/(\partial x)(xcos(x^2y))

Lösung

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

cos (x^{2} y) - 2 x^{2} y sin (x^{2} y)

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Produktregel an:

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

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

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

\frac{\partial}{\partial x} (x) = 1

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

= 1 \cdot cos (x^{2} y) + (- sin (x^{2} y) \cdot 2 y x) x

Vereinfache

1 \cdot cos (x^{2} y) + (- sin (x^{2} y) \cdot 2 y x) x : cos (x^{2} y) - 2 x^{2} y sin (x^{2} y)

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

\frac{d}{d y} (y^{3} + k x y^{4} - 2 x)

\int \frac{1}{x ^{2}} sin (\frac{1}{x}) cos (\frac{1}{x}) d x

\int_{0}^{2} 4 x^{2} - 2 x^{3} d x

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

a re a y = x^{2}, y = - x^{2} + 4 x