What is the derivative of ((x-1)^2)/(x-2) ?

The derivative of ((x-1)^2)/(x-2) is (x^2-4x+3)/((x-2)^2)

What is the first derivative of ((x-1)^2)/(x-2) ?

The first derivative of ((x-1)^2)/(x-2) is (x^2-4x+3)/((x-2)^2)

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derivative of

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

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

Solution steps

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

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

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

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

Simplify

\frac{2 ( x - 1 ) ( x - 2 ) - 1 \cdot ( x - 1 ) ^{2}}{( x - 2 ) ^{2}} : \frac{x ^{2} - 4 x + 3}{( x - 2 ) ^{2}}

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

(a + 2 x)^{7 x}

\frac{1 - t ^{4}}{4}

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

3 lo g_{10} (x) sin (x) + 7

\frac{1}{2 ^{x}}

What is the derivative of ((x-1)^2)/(x-2) ?
The derivative of ((x-1)^2)/(x-2) is (x^2-4x+3)/((x-2)^2)
What is the first derivative of ((x-1)^2)/(x-2) ?
The first derivative of ((x-1)^2)/(x-2) is (x^2-4x+3)/((x-2)^2)