What is (\partial)/(\partial x)((2x)/(x^2-2x)) ?

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

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(\partial)/(\partial x)((2x)/(x^2-2x))

\frac{\partial}{\partial x} (\frac{2 x}{x ^{2} - 2 x})

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

Solution steps

\frac{\partial}{\partial x} (\frac{2 x}{x ^{2} - 2 x})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

x \to 1 lim (sin (\frac{1}{x}))

\int (x^{2} \cdot sin (x)) d x

\frac{d}{d x} (x^{\frac{2}{3}} + y^{\frac{2}{3}})

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

\int_{- 2}^{0} x^{2} d x

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