(\partial)/(\partial x)(x(x+y))

Lösung

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

2 x + y

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Produktregel an:

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

f = x, g = x + y

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

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

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

= 1 \cdot (x + y) + 1 \cdot x

Vereinfache

1 \cdot (x + y) + 1 \cdot x : 2 x + y

= 2 x + y

\int_{- \infty}^{2} \frac{1}{x ^{2} + 1} d x

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

\int \frac{1}{e ^{z} + e ^{- z}} d z

\frac{d}{d x} ((3 + x - 2 x^{2})^{\frac{1}{4}})

im pl i c i t \frac{d y}{d x}, 4 x^{2} + 9 y^{2} = 36