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Popular >

derivative of ln((x-2/(x+2)))

Solution

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

Solution

\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 )}

Graph

Popular Examples

3y^{''}-10y^'+3y=0,y(0)=-5,y^'(0)=-1

3 y^{^{''}} - 10 y^{^{'}} + 3 y = 0, y (0) = - 5, y^{^{'}} (0) = - 1

integral from 0 to pi of sin^2(x)cos(x)

\int_{0}^{π} sin^{2} (x) cos (x) d x

tangent of f(x)=(6x-5)^{1/2},\at x=1 tangent of

f (x) = (6 x - 5)^{\frac{1}{2}}, at x = 1

(dy)/(dx)=8x^{-9}

\frac{d y}{d x} = 8 x^{- 9}

derivative of 2/3 x^3-3/(4x^2)

\frac{d}{d x} (\frac{2}{3} x^{3} - \frac{3}{4 x ^{2}})

Frequently Asked Questions (FAQ)

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))