What is the derivative of ((2x^2)/(x-2)) ?

The derivative of ((2x^2)/(x-2)) is (2(x^2-4x))/((x-2)^2)

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

The first derivative of ((2x^2)/(x-2)) is (2(x^2-4x))/((x-2)^2)

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

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

Solution steps

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

Take the constant out:

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

= 2 \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}}

= 2 \cdot \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}) = 2 x

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

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

Simplify

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

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

f (x) = x^{2} - 5

\frac{d}{d x} (3 cos (x) - 4 sin (x))

\frac{e ^{x}}{7 x ^{2} + 5}

x \to 9 lim (x^{2})

\int cos (t) d t

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