de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

(\partial)/(\partial x)(x^{(x^2+y^2)})

Lösung

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

Lösung

x^{x^{2} + y^{2}} (2 x ln (x) + \frac{x ^{2} + y ^{2}}{x})

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende Exponentenregel an:

a^{b} = e^{b l n (a)}

x^{x^{2} + y^{2}} = e^{(x^{2} + y^{2}) l n (x)}

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

Wende die Kettenregel an:

e^{(x^{2} + y^{2}) l n (x)} \frac{\partial}{\partial x} ((x^{2} + y^{2}) ln (x))

= e^{(x^{2} + y^{2}) l n (x)} \frac{\partial}{\partial x} ((x^{2} + y^{2}) ln (x))

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

= e^{(x^{2} + y^{2}) l n (x)} (2 x ln (x) + \frac{x ^{2} + y ^{2}}{x})

e^{(x^{2} + y^{2}) l n (x)} = x^{x^{2} + y^{2}}

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

Beliebte Beispiele

integral of (5-3x)^{10}

integral of (x^2arctan(x))/(x^2+1)

implicit e^{x/y}=5x-y

laplacetransform (t-2)^2

integral from 1 to 4 of (x^2+8)/(5x-x^2)