What is the derivative of (2x^2-5x+5)/(x-2) ?

The derivative of (2x^2-5x+5)/(x-2) is (2x^2-8x+5)/((x-2)^2)

What is the first derivative of (2x^2-5x+5)/(x-2) ?

The first derivative of (2x^2-5x+5)/(x-2) is (2x^2-8x+5)/((x-2)^2)

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derivative of

\frac{2 x ^{2} - 5 x + 5}{x - 2}

\frac{2 x ^{2} - 8 x + 5}{( x - 2 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{2 x ^{2} - 5 x + 5}{x - 2})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 2 x ^{2} - 5 x + 5 ) ( x - 2 ) - \frac{d}{d x} ( x - 2 ) ( 2 x ^{2} - 5 x + 5 )}{( x - 2 ) ^{2}}

\frac{d}{d x} (2 x^{2} - 5 x + 5) = 4 x - 5

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

= \frac{( 4 x - 5 ) ( x - 2 ) - 1 \cdot ( 2 x ^{2} - 5 x + 5 )}{( x - 2 ) ^{2}}

Simplify

\frac{( 4 x - 5 ) ( x - 2 ) - 1 \cdot ( 2 x ^{2} - 5 x + 5 )}{( x - 2 ) ^{2}} : \frac{2 x ^{2} - 8 x + 5}{( x - 2 ) ^{2}}

= \frac{2 x ^{2} - 8 x + 5}{( x - 2 ) ^{2}}

\frac{d}{d x} (f (x) sin (x))

x \to 0 lim (\frac{x}{8 x ^{2} - x})

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

f (x) = 2 (x)^{4}

f (x) = ln (3 x + 2)

What is the derivative of (2x^2-5x+5)/(x-2) ?
The derivative of (2x^2-5x+5)/(x-2) is (2x^2-8x+5)/((x-2)^2)
What is the first derivative of (2x^2-5x+5)/(x-2) ?
The first derivative of (2x^2-5x+5)/(x-2) is (2x^2-8x+5)/((x-2)^2)