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Popular >

derivative of sqrt(2-1/x)

Solution

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

Solution

\frac{1}{2 x ^{\frac{3}{2}} 2 x - 1}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

\frac{1}{2 2 - \frac{1}{x}} \cdot \frac{1}{x ^{2}} : \frac{1}{2 x ^{\frac{3}{2}} 2 x - 1}

= \frac{1}{2 x ^{\frac{3}{2}} 2 x - 1}

Graph

Popular Examples

integral of x/(sqrt(36-x^2))

\int \frac{x}{36 - x ^{2}} d x

integral of (5x^3+5x)/(x-1)

\int \frac{5 x ^{3} + 5 x}{x - 1} d x

d/(dt)(\sqrt[3]{t})

\frac{d}{d t} (3 t)

integral of x-1/2 sin(2x)

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

derivative of e^{(2x})

\frac{d}{d x} (e^{(2 x)})

Frequently Asked Questions (FAQ)

What is the derivative of sqrt(2-1/x) ?
The derivative of sqrt(2-1/x) is 1/(2x^{3/2)sqrt(2x-1)}
What is the first derivative of sqrt(2-1/x) ?
The first derivative of sqrt(2-1/x) is 1/(2x^{3/2)sqrt(2x-1)}