What is the derivative of sqrt(x-2\sqrt{x-2)} ?

The derivative of sqrt(x-2\sqrt{x-2)} is (sqrt(x-2)-1)/(2sqrt(x-2)\sqrt{x-2\sqrt{x-2)}}

What is the first derivative of sqrt(x-2\sqrt{x-2)} ?

The first derivative of sqrt(x-2\sqrt{x-2)} is (sqrt(x-2)-1)/(2sqrt(x-2)\sqrt{x-2\sqrt{x-2)}}

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

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

Solution steps

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

Apply the chain rule:

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

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

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

= \frac{1}{2 x - 2 x - 2} (1 - \frac{1}{x - 2})

Simplify

\frac{1}{2 x - 2 x - 2} (1 - \frac{1}{x - 2}) : \frac{x - 2 - 1}{2 x - 2 x - 2 x - 2}

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

What is the derivative of sqrt(x-2\sqrt{x-2)} ?
The derivative of sqrt(x-2\sqrt{x-2)} is (sqrt(x-2)-1)/(2sqrt(x-2)\sqrt{x-2\sqrt{x-2)}}
What is the first derivative of sqrt(x-2\sqrt{x-2)} ?
The first derivative of sqrt(x-2\sqrt{x-2)} is (sqrt(x-2)-1)/(2sqrt(x-2)\sqrt{x-2\sqrt{x-2)}}