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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\frac{d}{d x} (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 )}

\frac{\partial}{\partial x} (4 x^{0.5} + 2 x^{0.25})

\int 2 x e^{4 x} d x

y^{^{'}} + 3 (tan (3 x)) y = - 10 cos (3 x)

\int_{0}^{2} \int 1

\int \frac{6 x ^{3} - 12 x ^{2} + 5}{x ^{2} - 2 x} 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))