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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

\frac{1}{2 \frac{1 - 3 x}{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}}}

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