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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}}

Graph

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\int (\frac{9 + x + x}{x}) d x

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\int (2 x + 5) e^{x} d x

y^'-2xy=e^{x^2}

y^{^{'}} - 2 x y = e^{x^{2}}

integral of (2x^{10}+4x^9+x^8+10)

\int (2 x^{10} + 4 x^{9} + x^{8} + 10) d x

integral of x^2(x^2-6x+9)

\int x^{2} (x^{2} - 6 x + 9) d 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)