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Beliebt Rechnen >

derivative y=ln((x+3)/(x^2))

Lösung

ableitung von

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

Lösung

\frac{- x - 6}{x ( x + 3 )}

Schritte zur Lösung

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

Wende die Kettenregel an:

\frac{1}{\frac{x + 3}{x ^{2}}} \frac{d}{d x} (\frac{x + 3}{x ^{2}})

= \frac{1}{\frac{x + 3}{x ^{2}}} \frac{d}{d x} (\frac{x + 3}{x ^{2}})

\frac{d}{d x} (\frac{x + 3}{x ^{2}}) = \frac{- x - 6}{x ^{3}}

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

Vereinfache

\frac{1}{\frac{x + 3}{x ^{2}}} \cdot \frac{- x - 6}{x ^{3}} : \frac{- x - 6}{x ( x + 3 )}

= \frac{- x - 6}{x ( x + 3 )}

Graph

Beliebte Beispiele

derivative \sqrt[7]{x}-7e^x

d er i v a t i v e 7 x - 7 e^{x}

derivative of x^3sqrt(1-x^2)

\frac{d}{d x} (x^{3} 1 - x^{2})

sum from n=1 to infinity of (n!)/(3n!-1)

n = 1 \sum \infty \frac{n !}{3 n ! - 1}

fläche y=3x+1,y=13+2x-x^2

a re a y = 3 x + 1, y = 13 + 2 x - x^{2}

tangent f(x)=sqrt(2x+1),\at x=1

t an g e n t f (x) = 2 x + 1, at x = 1