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Popular >

derivative of f(x)=ln((1-x)/(1+x))

Solution

derivative of

f (x) = ln (\frac{1 - x}{1 + x})

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

(\partial)/(\partial x)((x+xy+y)^3)

\frac{\partial}{\partial x} ((x + x y + y)^{3})

integral of x(3x^2-7)^{-2}

\int x (3 x^{2} - 7)^{- 2} d x

derivative of 3/4 x^4-5x^2+4x+1

\frac{d}{d x} (\frac{3}{4} x^{4} - 5 x^{2} + 4 x + 1)

derivative of cos^2(2-x^2)

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

t^2y^{''}-3ty^'+3y=0,y(1)=5,y^'(1)=3

t^{2} y^{^{''}} - 3 t y^{^{'}} + 3 y = 0, y (1) = 5, y^{^{'}} (1) = 3

Frequently Asked Questions (FAQ)

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