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

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

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

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

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

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

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Quotient Rule:

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

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

\frac{d x}{d x} = 1

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

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

Simplify

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

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

y^{^{'}} + \frac{7 y}{x + 3} = (x + 3)^{3}

\int \frac{t}{( t ^{2} + 1 ) ^{\frac{3}{2}}} d t

\int \frac{13 x}{x + 3} d x

x \to 2 lim (\frac{5 x - 3}{4})

\int 25 x^{2} - 4 d x

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