What is (\partial)/(\partial x)((x-1)/(x+1)) ?

The answer to (\partial)/(\partial x)((x-1)/(x+1)) is 2/((x+1)^2)

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(\partial)/(\partial x)((x-1)/(x+1))

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

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

Solution steps

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

\frac{\partial}{\partial x} (x - 1) = 1

\frac{\partial}{\partial x} (x + 1) = 1

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

Simplify

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

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

\int_{0}^{\infty} \frac{1}{e ^{x} - 1} d x

\frac{d}{d t} (\frac{1}{6} t^{3})

\int (x x^{2} + 3) d x

y^{^{''}} + 36 y = - 60 sec (6 t)

\int 12 (y^{4} + 4 y^{2} + 8)^{2} (y^{3} + 2 y) d y

What is (\partial)/(\partial x)((x-1)/(x+1)) ?
The answer to (\partial)/(\partial x)((x-1)/(x+1)) is 2/((x+1)^2)