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

The derivative of sqrt((3x+1/(2x-1))) is -5/(2sqrt(3x+1)(2x-1)^{3/2)}

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

The first derivative of sqrt((3x+1/(2x-1))) is -5/(2sqrt(3x+1)(2x-1)^{3/2)}

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

- \frac{5}{2 3 x + 1 ( 2 x - 1 ) ^{\frac{3}{2}}}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (\frac{3 x + 1}{2 x - 1}) = - \frac{5}{( 2 x - 1 ) ^{2}}

= \frac{1}{2 \frac{3 x + 1}{2 x - 1}} (- \frac{5}{( 2 x - 1 ) ^{2}})

Simplify

\frac{1}{2 \frac{3 x + 1}{2 x - 1}} (- \frac{5}{( 2 x - 1 ) ^{2}}) : - \frac{5}{2 3 x + 1 ( 2 x - 1 ) ^{\frac{3}{2}}}

= - \frac{5}{2 3 x + 1 ( 2 x - 1 ) ^{\frac{3}{2}}}

\frac{1}{s ( s + 4 )}

(6 e^{x} cos (x)) (0.6)

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

\frac{\partial}{\partial x} (\frac{12 x}{6 x ^{2} + y ^{2} + 4})

\frac{d y}{d x}, x^{3} + y^{3} = 4 x y + 1

What is the derivative of sqrt((3x+1/(2x-1))) ?
The derivative of sqrt((3x+1/(2x-1))) is -5/(2sqrt(3x+1)(2x-1)^{3/2)}
What is the first derivative of sqrt((3x+1/(2x-1))) ?
The first derivative of sqrt((3x+1/(2x-1))) is -5/(2sqrt(3x+1)(2x-1)^{3/2)}