What is the derivative of (4x^2+3/(2x-1)) ?

The derivative of (4x^2+3/(2x-1)) is (8x^2-8x-6)/((2x-1)^2)

What is the first derivative of (4x^2+3/(2x-1)) ?

The first derivative of (4x^2+3/(2x-1)) is (8x^2-8x-6)/((2x-1)^2)

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

\frac{8 x ^{2} - 8 x - 6}{( 2 x - 1 ) ^{2}}

Solution steps

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

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

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

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

= \frac{8 x ( 2 x - 1 ) - 2 ( 4 x ^{2} + 3 )}{( 2 x - 1 ) ^{2}}

Expand

8 x (2 x - 1) - 2 (4 x^{2} + 3) : 8 x^{2} - 8 x - 6

= \frac{8 x ^{2} - 8 x - 6}{( 2 x - 1 ) ^{2}}

f (x) = x^{3} + y^{3} = 16

x = 5 - 5 \cdot y^{2}, x = 5 \cdot y^{2} - 5

\frac{d}{d x} (\frac{x ^{4} + 48}{24 x})

\frac{e ^{- π s}}{s}

x^{2} - 3 x, 3 x + 7, - 1, 7

What is the derivative of (4x^2+3/(2x-1)) ?
The derivative of (4x^2+3/(2x-1)) is (8x^2-8x-6)/((2x-1)^2)
What is the first derivative of (4x^2+3/(2x-1)) ?
The first derivative of (4x^2+3/(2x-1)) is (8x^2-8x-6)/((2x-1)^2)