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

The derivative of ln((x-2)/(x+2)) is 4/((x-2)(x+2))

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

The first derivative of ln((x-2)/(x+2)) is 4/((x-2)(x+2))

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derivative of

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

\frac{4}{( x - 2 ) ( x + 2 )}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (\frac{x - 2}{x + 2}) = \frac{4}{( x + 2 ) ^{2}}

= \frac{1}{\frac{x - 2}{x + 2}} \cdot \frac{4}{( x + 2 ) ^{2}}

Simplify

\frac{1}{\frac{x - 2}{x + 2}} \cdot \frac{4}{( x + 2 ) ^{2}} : \frac{4}{( x - 2 ) ( x + 2 )}

= \frac{4}{( x - 2 ) ( x + 2 )}

\int \frac{4 x ^{6} + 3 x ^{4}}{x ^{3}} d x

y^{'} = 0.0018 y (2400 - y)

\frac{\partial}{\partial x} (x^{3} y z^{2})

ln ∣ ln (x) ∣

\frac{d y}{d t} + \frac{1}{20} y = \frac{3}{2}, y (0) = 0

What is the derivative of ln((x-2)/(x+2)) ?
The derivative of ln((x-2)/(x+2)) is 4/((x-2)(x+2))
What is the first derivative of ln((x-2)/(x+2)) ?
The first derivative of ln((x-2)/(x+2)) is 4/((x-2)(x+2))