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)(xln(x/(y^2)))

Lösung

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

Lösung

ln (x) - 2 ln (y) + 1

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Produktregel an:

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

f = x, g = ln (\frac{x}{y ^{2}})

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

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

\frac{\partial}{\partial x} (ln (\frac{x}{y ^{2}})) = \frac{1}{x}

= 1 \cdot ln (\frac{x}{y ^{2}}) + \frac{1}{x} x

Vereinfache

1 \cdot ln (\frac{x}{y ^{2}}) + \frac{1}{x} x : ln (x) - 2 ln (y) + 1

= ln (x) - 2 ln (y) + 1

Beliebte Beispiele

(dy)/(dx)+4xy=8x^3

derivative of (cos(x)/5)

limit as x approaches infinity of (2x)/1

integral of (2x+3)/(x(x^2-4)^2)

(dy)/(dt)(t)+2y=3e^{-t}