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

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

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

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

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

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

Solution steps

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

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

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

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

Simplify

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

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

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