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

The derivative of ln((x+1/(sqrt(x-2)))) is (x-5)/(2(x+1)(x-2))

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

The first derivative of ln((x+1/(sqrt(x-2)))) is (x-5)/(2(x+1)(x-2))

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

\frac{x - 5}{2 ( x + 1 ) ( x - 2 )}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (\frac{x + 1}{x - 2}) = \frac{x - 5}{2 ( x - 2 ) x - 2}

= \frac{1}{\frac{x + 1}{x - 2}} \cdot \frac{x - 5}{2 ( x - 2 ) x - 2}

Simplify

\frac{1}{\frac{x + 1}{x - 2}} \cdot \frac{x - 5}{2 ( x - 2 ) x - 2} : \frac{x - 5}{2 ( x + 1 ) ( x - 2 )}

= \frac{x - 5}{2 ( x + 1 ) ( x - 2 )}

\int_{1}^{\infty} \frac{5}{x ^{4}} d x

\int (2 - x) d x

x \to 0 + lim (x^{\frac{1}{2}})

y^{^{'}} = \frac{( x ^{3} + y ^{3} )}{x y ^{2}}

4 y^{^{'}} + t y = 7

What is the derivative of ln((x+1/(sqrt(x-2)))) ?
The derivative of ln((x+1/(sqrt(x-2)))) is (x-5)/(2(x+1)(x-2))
What is the first derivative of ln((x+1/(sqrt(x-2)))) ?
The first derivative of ln((x+1/(sqrt(x-2)))) is (x-5)/(2(x+1)(x-2))