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_{- 3}^{5} 4 d x

f (x) = 4^{s i n (2) (x) + c o s (3 x)}

\frac{d}{d x} (\frac{x ^{2}}{x - 5})

\int \frac{1 - tan ( x )}{1 + tan ( x )} d x

x \to 0 lim (\frac{( x ^{3} )}{x ^{3}})

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))