(\partial)/(\partial x)(xy-y+sin(1))

Lösung

\frac{\partial}{\partial x} (x y - y + sin (1))

y

Schritte zur Lösung

\frac{\partial}{\partial x} (x y - y + sin (1))

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{\partial}{\partial x} (x y) - \frac{\partial}{\partial x} (y) + \frac{\partial}{\partial x} (sin (1))

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

\frac{\partial}{\partial x} (y) = 0

\frac{\partial}{\partial x} (sin (1)) = 0

= y - 0 + 0

Vereinfache

= y

\int_{0}^{2} 2^{- θ} d θ

\int sin^{3} (4 x) cos (4 x) d x

\frac{\partial}{\partial x} (x^{- 1} y^{2} + x y^{2} + 5 x y)

\int_{1}^{16} \frac{1}{8 - x} d x

\frac{d y}{d x} + 2 x y = y + 4 x - 2