derivative of 1/(x(ln(x)))

Lösung

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

- \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 )}

81 y^{^{''}} + 108 y^{^{'}} + 66 y = 0, y^{^{'}} (0) = 2, y (0) = 6

t an g e n t 1 - x

\frac{d}{d x} (\frac{9 x}{64 + x ^{2} + y ^{2}})

\frac{d}{d x} (- ln ∣ cos (x) ∣)

d er i v a t i v e f (x) = (- 3 x^{2} - 3)^{4}