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

The derivative of (ln(1-x^2)/(x^2)) is -(2(x^2+ln(-x^2+1)(-x^2+1)))/(x^3(-x^2+1))

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

The first derivative of (ln(1-x^2)/(x^2)) is -(2(x^2+ln(-x^2+1)(-x^2+1)))/(x^3(-x^2+1))

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

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

Solution steps

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

\frac{d}{d x} (x^{2}) = 2 x

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

Simplify

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

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

\int \frac{cot ( ln ( x ^{4} + 1 ) ) x ^{3}}{x ^{4} + 1} d x

\int \frac{1}{x ^{2} + 12} d x

3 x, 9 x^{2}

n = 1 \sum \infty \frac{2 n}{1 1 ^{n}}

\frac{d}{d x} (\frac{4 2}{3} x^{\frac{3}{2}} - 1)

What is the derivative of (ln(1-x^2)/(x^2)) ?
The derivative of (ln(1-x^2)/(x^2)) is -(2(x^2+ln(-x^2+1)(-x^2+1)))/(x^3(-x^2+1))
What is the first derivative of (ln(1-x^2)/(x^2)) ?
The first derivative of (ln(1-x^2)/(x^2)) is -(2(x^2+ln(-x^2+1)(-x^2+1)))/(x^3(-x^2+1))