What is the derivative of sqrt(((2x-7)/(2+3x))) ?

The derivative of sqrt(((2x-7)/(2+3x))) is (25)/(2sqrt(2x-7)(3x+2)^{3/2)}

What is the first derivative of sqrt(((2x-7)/(2+3x))) ?

The first derivative of sqrt(((2x-7)/(2+3x))) is (25)/(2sqrt(2x-7)(3x+2)^{3/2)}

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derivative of

(\frac{2 x - 7}{2 + 3 x})

\frac{25}{2 2 x - 7 ( 3 x + 2 ) ^{\frac{3}{2}}}

Solution steps

\frac{d}{d x} (\frac{2 x - 7}{2 + 3 x})

Apply the chain rule:

\frac{1}{2 \frac{2 x - 7}{2 + 3 x}} \frac{d}{d x} (\frac{2 x - 7}{2 + 3 x})

= \frac{1}{2 \frac{2 x - 7}{2 + 3 x}} \frac{d}{d x} (\frac{2 x - 7}{2 + 3 x})

\frac{d}{d x} (\frac{2 x - 7}{2 + 3 x}) = \frac{25}{( 2 + 3 x ) ^{2}}

= \frac{1}{2 \frac{2 x - 7}{2 + 3 x}} \cdot \frac{25}{( 2 + 3 x ) ^{2}}

Simplify

\frac{1}{2 \frac{2 x - 7}{2 + 3 x}} \cdot \frac{25}{( 2 + 3 x ) ^{2}} : \frac{25}{2 2 x - 7 ( 3 x + 2 ) ^{\frac{3}{2}}}

= \frac{25}{2 2 x - 7 ( 3 x + 2 ) ^{\frac{3}{2}}}

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What is the derivative of sqrt(((2x-7)/(2+3x))) ?
The derivative of sqrt(((2x-7)/(2+3x))) is (25)/(2sqrt(2x-7)(3x+2)^{3/2)}
What is the first derivative of sqrt(((2x-7)/(2+3x))) ?
The first derivative of sqrt(((2x-7)/(2+3x))) is (25)/(2sqrt(2x-7)(3x+2)^{3/2)}