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

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

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

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

\frac{d}{d x} (ln (g (x) (3 x^{2})))

\frac{d}{d x} (e^{2 x} sin (x))

\int \frac{y}{( y + 5 ) ( 2 y - 1 )} d y

f (t) = ln (1 + 2 \cdot t)

\int \frac{7}{( x - 10 ) ^{7}} d x

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