What is the derivative of y=(x^2-7x+2)/(x-2) ?

The derivative of y=(x^2-7x+2)/(x-2) is (x^2-4x+12)/((x-2)^2)

What is the first derivative of y=(x^2-7x+2)/(x-2) ?

The first derivative of y=(x^2-7x+2)/(x-2) is (x^2-4x+12)/((x-2)^2)

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derivative of

y = \frac{x ^{2} - 7 x + 2}{x - 2}

\frac{x ^{2} - 4 x + 12}{( x - 2 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x ^{2} - 7 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} - 7 x + 2 ) ( x - 2 ) - \frac{d}{d x} ( x - 2 ) ( x ^{2} - 7 x + 2 )}{( x - 2 ) ^{2}}

\frac{d}{d x} (x^{2} - 7 x + 2) = 2 x - 7

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

= \frac{( 2 x - 7 ) ( x - 2 ) - 1 \cdot ( x ^{2} - 7 x + 2 )}{( x - 2 ) ^{2}}

Simplify

\frac{( 2 x - 7 ) ( x - 2 ) - 1 \cdot ( x ^{2} - 7 x + 2 )}{( x - 2 ) ^{2}} : \frac{x ^{2} - 4 x + 12}{( x - 2 ) ^{2}}

= \frac{x ^{2} - 4 x + 12}{( x - 2 ) ^{2}}

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

f (x) = x^{2} + 2, [- 2, 1]

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

\int (3 x^{11}) d x

\int (x^{\frac{3}{2}} + 3)^{7} x d x

What is the derivative of y=(x^2-7x+2)/(x-2) ?
The derivative of y=(x^2-7x+2)/(x-2) is (x^2-4x+12)/((x-2)^2)
What is the first derivative of y=(x^2-7x+2)/(x-2) ?
The first derivative of y=(x^2-7x+2)/(x-2) is (x^2-4x+12)/((x-2)^2)