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Beliebt Rechnen >

derivative of (3x^2/(ln(x)))

Lösung

\frac{d}{d x} (\frac{3 x ^{2}}{ln ( x )})

Lösung

\frac{3 ( 2 x ln ( x ) - x )}{ln ^{2} ( x )}

Schritte zur Lösung

\frac{d}{d x} (\frac{3 x ^{2}}{ln ( x )})

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= 3 \frac{d}{d x} (\frac{x ^{2}}{ln ( x )})

Wende die Quotientenregel an:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= 3 \cdot \frac{\frac{d}{d x} ( x ^{2} ) ln ( x ) - \frac{d}{d x} ( ln ( x ) ) x ^{2}}{( ln ( x ) ) ^{2}}

\frac{d}{d x} (x^{2}) = 2 x

\frac{d}{d x} (ln (x)) = \frac{1}{x}

= 3 \cdot \frac{2 x ln ( x ) - \frac{1}{x} x ^{2}}{( ln ( x ) ) ^{2}}

Vereinfache

3 \cdot \frac{2 x ln ( x ) - \frac{1}{x} x ^{2}}{ln ^{2} ( x )} : \frac{3 ( 2 x ln ( x ) - x )}{ln ^{2} ( x )}

= \frac{3 ( 2 x ln ( x ) - x )}{ln ^{2} ( x )}

Graph

Beliebte Beispiele

(dy)/(dx)=(x+y)^2-1,y(3)=4

\frac{d y}{d x} = (x + y)^{2} - 1, y (3) = 4

integral from 0 to 1 of 2(1+sqrt(x))^8

\int_{0}^{1} 2 (1 + x)^{8} d x

derivative ((x+2))/((x-2))

d er i v a t i v e \frac{( x + 2 )}{( x - 2 )}

limit as x approaches 3 of (2^x-8)/(3-x)

x \to 3 lim (\frac{2 ^{x} - 8}{3 - x})

fläche y=4x,y=4,y= 4/9 x^24

a re a y = 4 x, y = 4, y = \frac{4}{9} x^{2} 4