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

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

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

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

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derivative of

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int \frac{4 x}{2 x + 1} d x

\int x^{9} d x

y = x + e^{2 x}

x^{3}, x, - 1, 1

\int 6 x^{5} sin (x^{6}) d x

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