What is the derivative of (4x-6)/(2x^2+x-2) ?

The derivative of (4x-6)/(2x^2+x-2) is (-8x^2+24x-2)/((2x^2+x-2)^2)

What is the first derivative of (4x-6)/(2x^2+x-2) ?

The first derivative of (4x-6)/(2x^2+x-2) is (-8x^2+24x-2)/((2x^2+x-2)^2)

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derivative of

\frac{4 x - 6}{2 x ^{2} + x - 2}

\frac{- 8 x ^{2} + 24 x - 2}{( 2 x ^{2} + x - 2 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{4 x - 6}{2 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} ( 4 x - 6 ) ( 2 x ^{2} + x - 2 ) - \frac{d}{d x} ( 2 x ^{2} + x - 2 ) ( 4 x - 6 )}{( 2 x ^{2} + x - 2 ) ^{2}}

\frac{d}{d x} (4 x - 6) = 4

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

= \frac{4 ( 2 x ^{2} + x - 2 ) - ( 4 x + 1 ) ( 4 x - 6 )}{( 2 x ^{2} + x - 2 ) ^{2}}

Expand

4 (2 x^{2} + x - 2) - (4 x + 1) (4 x - 6) : - 8 x^{2} + 24 x - 2

= \frac{- 8 x ^{2} + 24 x - 2}{( 2 x ^{2} + x - 2 ) ^{2}}

\int \frac{8 x ^{2}}{25 - x ^{2}} d x

\frac{d}{d x} (e^{3 y - x^{2}})

\int (2 x - 4)^{5} d x

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

\frac{d}{d x} (e^{t a n (3 x)})

What is the derivative of (4x-6)/(2x^2+x-2) ?
The derivative of (4x-6)/(2x^2+x-2) is (-8x^2+24x-2)/((2x^2+x-2)^2)
What is the first derivative of (4x-6)/(2x^2+x-2) ?
The first derivative of (4x-6)/(2x^2+x-2) is (-8x^2+24x-2)/((2x^2+x-2)^2)