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

The derivative of (x^2+x-2/(x^2-3x+4)) is (-4x^2+12x-2)/((x^2-3x+4)^2)

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

The first derivative of (x^2+x-2/(x^2-3x+4)) is (-4x^2+12x-2)/((x^2-3x+4)^2)

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

\frac{- 4 x ^{2} + 12 x - 2}{( x ^{2} - 3 x + 4 ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Expand

(2 x + 1) (x^{2} - 3 x + 4) - (2 x - 3) (x^{2} + x - 2) : - 4 x^{2} + 12 x - 2

= \frac{- 4 x ^{2} + 12 x - 2}{( x ^{2} - 3 x + 4 ) ^{2}}

\int \frac{2 x + 3}{x ^{2} + 3 x} d x

\int (4 w - 1)^{3} d w

\frac{\partial}{\partial x} (e^{(x + y)})

\frac{\partial}{\partial x} (10 x y - 16 x)

\frac{d}{d x} (0.5 x)

What is the derivative of (x^2+x-2/(x^2-3x+4)) ?
The derivative of (x^2+x-2/(x^2-3x+4)) is (-4x^2+12x-2)/((x^2-3x+4)^2)
What is the first derivative of (x^2+x-2/(x^2-3x+4)) ?
The first derivative of (x^2+x-2/(x^2-3x+4)) is (-4x^2+12x-2)/((x^2-3x+4)^2)