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)(ln(3x^2+4y^2+2))

Lösung

\frac{\partial}{\partial x} (ln (3 x^{2} + 4 y^{2} + 2))

Lösung

\frac{6 x}{3 x ^{2} + 4 y ^{2} + 2}

Schritte zur Lösung

\frac{\partial}{\partial x} (ln (3 x^{2} + 4 y^{2} + 2))

Behandle

y

als Konstante

Wende die Kettenregel an:

\frac{1}{3 x ^{2} + 4 y ^{2} + 2} \frac{\partial}{\partial x} (3 x^{2} + 4 y^{2} + 2)

= \frac{1}{3 x ^{2} + 4 y ^{2} + 2} \frac{\partial}{\partial x} (3 x^{2} + 4 y^{2} + 2)

\frac{\partial}{\partial x} (3 x^{2} + 4 y^{2} + 2) = 6 x

= \frac{1}{3 x ^{2} + 4 y ^{2} + 2} \cdot 6 x

Vereinfache

\frac{1}{3 x ^{2} + 4 y ^{2} + 2} \cdot 6 x : \frac{6 x}{3 x ^{2} + 4 y ^{2} + 2}

= \frac{6 x}{3 x ^{2} + 4 y ^{2} + 2}

Beliebte Beispiele

sum from n=1 to infinity of x^n

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

integral of x^6e^{-x}

\int x^{6} e^{- x} d x

(\partial)/(\partial y)(cos(yx^2))

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

derivative-(12)/(x^6)

d er i v a t i v e - \frac{12}{x ^{6}}

derivative cos(4x^2)

d er i v a t i v e cos (4 x^{2})