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

The derivative of sqrt((2x/(4x-3))) is -3/(sqrt(2)\sqrt{x)(4x-3)^{3/2}}

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

The first derivative of sqrt((2x/(4x-3))) is -3/(sqrt(2)\sqrt{x)(4x-3)^{3/2}}

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

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

Solution steps

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

Apply the chain rule:

\frac{1}{2 \frac{2 x}{4 x - 3}} \frac{d}{d x} (\frac{2 x}{4 x - 3})

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

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

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

Simplify

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

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

14 t - sin (7 t)

\int (e^{x} cos (x)) d x

x \to 2 lim (x (x - 1))

What is the derivative of sqrt((2x/(4x-3))) ?
The derivative of sqrt((2x/(4x-3))) is -3/(sqrt(2)\sqrt{x)(4x-3)^{3/2}}
What is the first derivative of sqrt((2x/(4x-3))) ?
The first derivative of sqrt((2x/(4x-3))) is -3/(sqrt(2)\sqrt{x)(4x-3)^{3/2}}