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Popular >

derivative of (1-x/(1+x))

Solution

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

Solution

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

Popular Examples

limit as x approaches 0 of 4/x-4/(e^x-1)

x \to 0 lim (\frac{4}{x} - \frac{4}{e ^{x} - 1})

(\partial)/(\partial x)((6x+3y)ey)

\frac{\partial}{\partial x} ((6 x + 3 y) ey)

integral of 1/((x-3)(x+2))

\int \frac{1}{( x - 3 ) ( x + 2 )} d x

tangent of f(x)=x^2+6,(4,22)tangent of

f (x) = x^{2} + 6, (4, 22)

slope of (1,6),(0.5,8)slope

(1, 6), (0.5, 8)

Frequently Asked Questions (FAQ)

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