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

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

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

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

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derivative of

\frac{x + 3}{x - 3}

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

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (\frac{x + 3}{x - 3}) = - \frac{6}{( x - 3 ) ^{2}}

= \frac{1}{2 \frac{x + 3}{x - 3}} (- \frac{6}{( x - 3 ) ^{2}})

Simplify

\frac{1}{2 \frac{x + 3}{x - 3}} (- \frac{6}{( x - 3 ) ^{2}}) : - \frac{3}{x + 3 ( x - 3 ) ^{\frac{3}{2}}}

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

\frac{\partial}{\partial y} (4 x + y)

7 t^{3}

\int \frac{e ^{x}}{( e ^{x} - 5 ) ( e ^{2 x} + 1 )} d x

\frac{\partial}{\partial y} (2 x^{2} y^{3})

\frac{d}{d x} (2 x^{4} - 2 x)

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