vereinfachen derivative of 1/(ln(x^2))-ln(1/(x^2))

Lösung

vereinfachen

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

\frac{d}{d x} (\frac{1}{2 ln ( x )}) + 2 ln (x)

Schritte zur Lösung

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

Wende die log Regel an:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

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

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

Wende die log Regel an:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln (x^{2}) = 2 ln (x)

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

Wende die log Regel an:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln (x^{2}) = 2 ln (x)

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

- (ln (1) - 2 ln (x)) = 2 ln (x)

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

s im pl i f y \frac{\frac{3}{2} ln b ^{3} + 1 - ln ∣ 3 b + 1 ∣}{3}

s im pl i f y - \frac{1}{2} ln (\frac{1}{4})

s im pl i f y ln (\frac{a + a ^{2} + x ^{2}}{x})

s im pl i f y - ln (3) - ln (x) - ln (5 x)

s im pl i f y - lo g_{2} (\frac{1}{10})