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Popular >

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

Solution

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

Solution

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

Popular Examples

derivative of y=xe^{ax}derivative of

y = x e^{a x}

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

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

limit as x approaches-2 of x^2-5

x \to - 2 lim (x^{2} - 5)

integral from 1 to infinity of x^{-4/5}

\int_{1}^{\infty} x^{- \frac{4}{5}} d x

f^{^{'}} (x) = 6 x

Frequently Asked Questions (FAQ)

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