de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

(\partial)/(\partial r)(rln(rs^2t^3))

Lösung

\frac{\partial}{\partial r} (r ln (r s^{2} t^{3}))

Lösung

ln (r s^{2} t^{3}) + 1

Schritte zur Lösung

\frac{\partial}{\partial r} (r ln (r s^{2} t^{3}))

Behandle

s, t

als Konstanten

Wende die Produktregel an:

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

f = r, g = ln (r s^{2} t^{3})

= \frac{\partial}{\partial r} (r) ln (r s^{2} t^{3}) + \frac{\partial}{\partial r} (ln (r s^{2} t^{3})) r

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

\frac{\partial}{\partial r} (ln (r s^{2} t^{3})) = \frac{1}{r}

= 1 \cdot ln (r s^{2} t^{3}) + \frac{1}{r} r

Vereinfache

1 \cdot ln (r s^{2} t^{3}) + \frac{1}{r} r : ln (r s^{2} t^{3}) + 1

= ln (r s^{2} t^{3}) + 1

Beliebte Beispiele

limit as x approaches+1 of x(x-2)

x \to + 1 lim (x (x - 2))

derivative of sin(2arcsin(x))

\frac{d}{d x} (sin (2 arcsin (x)))

limit as x approaches 0 of x-4/x

x \to 0 lim (x - \frac{4}{x})

(2y+3x)dx+xdy=0

(2 y + 3 x) d x + x d y = 0

integral of (2+x^6)^86x^5

\int (2 + x^{6})^{8} 6 x^{5} d x