What is the derivative of (4x^2+3x/(2x-7)) ?

The derivative of (4x^2+3x/(2x-7)) is (8x^2-56x-21)/((2x-7)^2)

What is the first derivative of (4x^2+3x/(2x-7)) ?

The first derivative of (4x^2+3x/(2x-7)) is (8x^2-56x-21)/((2x-7)^2)

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\frac{d}{d x} (\frac{4 x ^{2} + 3 x}{2 x - 7})

\frac{8 x ^{2} - 56 x - 21}{( 2 x - 7 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{4 x ^{2} + 3 x}{2 x - 7})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 4 x ^{2} + 3 x ) ( 2 x - 7 ) - \frac{d}{d x} ( 2 x - 7 ) ( 4 x ^{2} + 3 x )}{( 2 x - 7 ) ^{2}}

\frac{d}{d x} (4 x^{2} + 3 x) = 8 x + 3

\frac{d}{d x} (2 x - 7) = 2

= \frac{( 8 x + 3 ) ( 2 x - 7 ) - 2 ( 4 x ^{2} + 3 x )}{( 2 x - 7 ) ^{2}}

Expand

(8 x + 3) (2 x - 7) - 2 (4 x^{2} + 3 x) : 8 x^{2} - 56 x - 21

= \frac{8 x ^{2} - 56 x - 21}{( 2 x - 7 ) ^{2}}

What is the derivative of (4x^2+3x/(2x-7)) ?
The derivative of (4x^2+3x/(2x-7)) is (8x^2-56x-21)/((2x-7)^2)
What is the first derivative of (4x^2+3x/(2x-7)) ?
The first derivative of (4x^2+3x/(2x-7)) is (8x^2-56x-21)/((2x-7)^2)