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Popular >

derivative of sqrt(x-2\sqrt{x-2)}

Solution

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

Solution

\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}

Popular Examples

derivative of (1+x^{1/2})

\frac{d}{d x} ((1 + x)^{\frac{1}{2}})

integral of (cos(x))^2*sin(x)

\int (cos (x))^{2} \cdot sin (x) d x

derivative of x^2-x-ln(x)

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

integral from-1 to 2 of (8-x^2)

\int_{- 1}^{2} (8 - x^{2}) d x

(\partial)/(\partial x)((5x+9y)^{10})

\frac{\partial}{\partial x} ((5 x + 9 y)^{10})

Frequently Asked Questions (FAQ)

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)}}