What is the derivative of (2x/(sqrt(4x-1))) ?

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

What is the first derivative of (2x/(sqrt(4x-1))) ?

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

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

\frac{2 ( 2 x - 1 )}{( 4 x - 1 ) 4 x - 1}

Solution steps

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

Take the constant out:

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

= 2 \frac{d}{d x} (\frac{x}{4 x - 1})

Apply the Quotient Rule:

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

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

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

\frac{d}{d x} (4 x - 1) = \frac{2}{4 x - 1}

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

Simplify

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

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

y, (9 x e^{- \frac{1}{y ^{3}}} - 20 x^{3})

\frac{d}{d x} ((3 - 2 x)^{5})

\frac{d y}{d x} = \frac{y}{( x + y )}

\int \frac{sec ( x ) tan ( x )}{sec ( x ) + 100} d x

\int arcsin (5 x) d x

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