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

The derivative of x/(sqrt(2x-1)) is (x-1)/((2x-1)sqrt(2x-1))

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

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

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derivative of

\frac{x}{2 x - 1}

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

Solution steps

\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}}

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

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

Simplify

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

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

\frac{d y}{d x} = x y + 3 x + 4 y + 12

\int ln (3 x - 2) d x

\int x^{3} + sin (x) d x

\frac{d}{d x} (\frac{sin ( x )}{x})

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

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