What is the derivative of (x^2+2x-8)/(x-1) ?

The derivative of (x^2+2x-8)/(x-1) is (x^2-2x+6)/((x-1)^2)

What is the first derivative of (x^2+2x-8)/(x-1) ?

The first derivative of (x^2+2x-8)/(x-1) is (x^2-2x+6)/((x-1)^2)

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derivative of

\frac{x ^{2} + 2 x - 8}{x - 1}

\frac{x ^{2} - 2 x + 6}{( x - 1 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x ^{2} + 2 x - 8}{x - 1})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x ^{2} + 2 x - 8 ) ( x - 1 ) - \frac{d}{d x} ( x - 1 ) ( x ^{2} + 2 x - 8 )}{( x - 1 ) ^{2}}

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

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

= \frac{( 2 x + 2 ) ( x - 1 ) - 1 \cdot ( x ^{2} + 2 x - 8 )}{( x - 1 ) ^{2}}

Simplify

\frac{( 2 x + 2 ) ( x - 1 ) - 1 \cdot ( x ^{2} + 2 x - 8 )}{( x - 1 ) ^{2}} : \frac{x ^{2} - 2 x + 6}{( x - 1 ) ^{2}}

= \frac{x ^{2} - 2 x + 6}{( x - 1 ) ^{2}}

\int \frac{a ^{l n (x)}}{x} d x

\frac{1}{1 - 5 x ^{2}}

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

\int \frac{1}{( x ^{2} - 1 ) ^{3}} d x

y^{^{''}} + \frac{14}{t} y^{^{'}} + \frac{42}{t ^{2}} y = 0

What is the derivative of (x^2+2x-8)/(x-1) ?
The derivative of (x^2+2x-8)/(x-1) is (x^2-2x+6)/((x-1)^2)
What is the first derivative of (x^2+2x-8)/(x-1) ?
The first derivative of (x^2+2x-8)/(x-1) is (x^2-2x+6)/((x-1)^2)