What is derivative of 1/(ln(x^2))-ln(1/(x^2)) ?

The solution to derivative of 1/(ln(x^2))-ln(1/(x^2)) is derivative of 1/(2ln(x))+2ln(x)

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

simplify

\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)

Solution steps

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

Apply log rule:

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))

Apply log rule:

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}))

Apply log rule:

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)

\frac{\frac{3}{2} ln b ^{3} + 1 - ln ∣ 3 b + 1 ∣}{3}

- \frac{1}{2} ln (\frac{1}{4})

ln (\frac{273}{264})

ln (\frac{a + a ^{2} + x ^{2}}{x})

- ln (3) - ln (x) - ln (5 x)

What is derivative of 1/(ln(x^2))-ln(1/(x^2)) ?
The solution to derivative of 1/(ln(x^2))-ln(1/(x^2)) is derivative of 1/(2ln(x))+2ln(x)