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

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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

= \frac{( 6 x + 2 ) ( 4 x - 2 ) - 4 ( 3 x ^{2} + 2 x )}{( 4 x - 2 ) ^{2}}

Simplify

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

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

ma c l a u r in ln (3 + x)

\int \frac{1}{x ^{2} x ^{2} - 25} d x

d er i v a t i v e f (x) = 3 sin (x) + 3 cos (x)

s l o p e (- 4, 8), (- 3, 8)

d er i v a t i v e sin (\frac{1}{x ^{2}})

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