What is the derivative of sqrt((3x+2/(5-4x))) ?

The derivative of sqrt((3x+2/(5-4x))) is (23)/(2sqrt(3x+2)(-4x+5)^{3/2)}

What is the first derivative of sqrt((3x+2/(5-4x))) ?

The first derivative of sqrt((3x+2/(5-4x))) is (23)/(2sqrt(3x+2)(-4x+5)^{3/2)}

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\frac{d}{d x} (\frac{3 x + 2}{5 - 4 x})

\frac{23}{2 3 x + 2 ( - 4 x + 5 ) ^{\frac{3}{2}}}

Solution steps

\frac{d}{d x} (\frac{3 x + 2}{5 - 4 x})

Apply the chain rule:

\frac{1}{2 \frac{3 x + 2}{5 - 4 x}} \frac{d}{d x} (\frac{3 x + 2}{5 - 4 x})

= \frac{1}{2 \frac{3 x + 2}{5 - 4 x}} \frac{d}{d x} (\frac{3 x + 2}{5 - 4 x})

\frac{d}{d x} (\frac{3 x + 2}{5 - 4 x}) = \frac{23}{( 5 - 4 x ) ^{2}}

= \frac{1}{2 \frac{3 x + 2}{5 - 4 x}} \cdot \frac{23}{( 5 - 4 x ) ^{2}}

Simplify

\frac{1}{2 \frac{3 x + 2}{5 - 4 x}} \cdot \frac{23}{( 5 - 4 x ) ^{2}} : \frac{23}{2 3 x + 2 ( - 4 x + 5 ) ^{\frac{3}{2}}}

= \frac{23}{2 3 x + 2 ( - 4 x + 5 ) ^{\frac{3}{2}}}

What is the derivative of sqrt((3x+2/(5-4x))) ?
The derivative of sqrt((3x+2/(5-4x))) is (23)/(2sqrt(3x+2)(-4x+5)^{3/2)}
What is the first derivative of sqrt((3x+2/(5-4x))) ?
The first derivative of sqrt((3x+2/(5-4x))) is (23)/(2sqrt(3x+2)(-4x+5)^{3/2)}