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

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

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

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

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derivative of

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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