What is the derivative of (x-1/x) ?

The derivative of (x-1/x) is 1/(x^2)

What is the first derivative of (x-1/x) ?

The first derivative of (x-1/x) is 1/(x^2)

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

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

Solution steps

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

\frac{d x}{d x} = 1

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

Simplify

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

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

x \to 0 lim (\frac{9}{x} - \frac{9}{x ^{2} - x})

ln (x) cos (x)

f (x) = (1 + 4 x)^{(\frac{3}{2})}, at x = 2

6 x^{2} - 4 x

\int \frac{1}{x ^{9}} d x

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