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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (\frac{2}{4 x + 3}) = - \frac{8}{( 4 x + 3 ) ^{2}}

= \frac{1}{2 \frac{2}{4 x + 3}} (- \frac{8}{( 4 x + 3 ) ^{2}})

Simplify

\frac{1}{2 \frac{2}{4 x + 3}} (- \frac{8}{( 4 x + 3 ) ^{2}}) : - \frac{2 2}{( 4 x + 3 ) ^{\frac{3}{2}}}

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

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