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Beliebt Rechnen >

derivative 1/(xln(x))

Lösung

ableitung von

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

Lösung

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

Schritte zur Lösung

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

Wende Exponentenregel an:

\frac{1}{a} = a^{- 1}

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

Graph

Beliebte Beispiele

integral from 0 to pi of 17sin^2(4x)

\int_{0}^{π} 17 sin^{2} (4 x) d x

y^{'''}+4y^'=3x-1

y^{^{'''}} + 4 y^{^{'}} = 3 x - 1

integral of (x^3-3x+\sqrt[4]{x}-5)

\int (x^{3} - 3 x + 4 x - 5) d x

tangent y= 1/(5+2x),(-1, 1/3)

t an g e n t y = \frac{1}{5 + 2 x}, (- 1, \frac{1}{3})

x(dy)/(dx)=sqrt(x^2-y^2)+y

x \frac{d y}{d x} = x^{2} - y^{2} + y