(\partial)/(\partial x)(x^2e^y+x-2y)

Lösung

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

2 e^{y} x + 1

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

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

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

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

\frac{\partial}{\partial x} (2 y) = 0

= 2 e^{y} x + 1 - 0

Vereinfache

= 2 e^{y} x + 1

\int \frac{x ^{2} + 2 x + 1}{x ^{3} + x} d x

\frac{d y}{d x} = e^{y - x^{2} + 1}

n = 1 \sum \infty \frac{1}{4 n + 2}

d er i v a t i v e g (u) = 3 u + 5 u

\int \frac{a}{x ^{a + 1}} d x