What is the derivative of (x^2-8x/(2x-3)) ?

The derivative of (x^2-8x/(2x-3)) is (2x^2-6x+24)/((2x-3)^2)

What is the first derivative of (x^2-8x/(2x-3)) ?

The first derivative of (x^2-8x/(2x-3)) is (2x^2-6x+24)/((2x-3)^2)

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\frac{d}{d x} (\frac{x ^{2} - 8 x}{2 x - 3})

\frac{2 x ^{2} - 6 x + 24}{( 2 x - 3 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x ^{2} - 8 x}{2 x - 3})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x ^{2} - 8 x ) ( 2 x - 3 ) - \frac{d}{d x} ( 2 x - 3 ) ( x ^{2} - 8 x )}{( 2 x - 3 ) ^{2}}

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

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

= \frac{( 2 x - 8 ) ( 2 x - 3 ) - 2 ( x ^{2} - 8 x )}{( 2 x - 3 ) ^{2}}

Expand

(2 x - 8) (2 x - 3) - 2 (x^{2} - 8 x) : 2 x^{2} - 6 x + 24

= \frac{2 x ^{2} - 6 x + 24}{( 2 x - 3 ) ^{2}}

\int - \frac{1}{2 x} d x

\frac{6 x}{4 - x ^{2}}, at x = 0

\frac{d}{d x} (4 7 x^{2} + 9)

\int \frac{x}{x ^{2} + 4} d x

5 x (x^{3} - 5 x + 5)

What is the derivative of (x^2-8x/(2x-3)) ?
The derivative of (x^2-8x/(2x-3)) is (2x^2-6x+24)/((2x-3)^2)
What is the first derivative of (x^2-8x/(2x-3)) ?
The first derivative of (x^2-8x/(2x-3)) is (2x^2-6x+24)/((2x-3)^2)