(\partial)/(\partial x)(3x+y+e^x+2e^y)

Lösung

\frac{\partial}{\partial x} (3 x + y + e^{x} + 2 e^{y})

e^{x} + 3

Schritte zur Lösung

\frac{\partial}{\partial x} (3 x + y + e^{x} + 2 e^{y})

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial x} (3 x) + \frac{\partial}{\partial x} (y) + \frac{\partial}{\partial x} (e^{x}) + \frac{\partial}{\partial x} (2 e^{y})

\frac{\partial}{\partial x} (3 x) = 3

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

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

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

= 3 + 0 + e^{x} + 0

Vereinfache

= e^{x} + 3

y^{^{'''}} - y^{^{'}} = x

\int \frac{4 x}{e ^{2 x}} d x

\int 24 x^{3} - 18 x^{2} + 8 x d x

\frac{d}{d x} (e^{1 - 2 x})

n = 1 \sum \infty 2^{n} x^{n} n!