Solve {c}{x-1/x}{-x-1/x}

$$\left. \begin{array} { c } { x - \frac { 1 } { x } } \\ { - x - \frac { 1 } { x } } \end{array} \right.$$

Evaluate

$$-\frac{2}{x}$$

Solution Steps

Combine x and -x to get 0.

$$-\frac{1}{x}-\frac{1}{x}$$

Combine -\frac{1}{x} and -\frac{1}{x} to get 2\left(-\frac{1}{x}\right).

$$2\left(-\frac{1}{x}\right)$$

Express 2\left(-\frac{1}{x}\right) as a single fraction.

$$\frac{-2}{x}$$

Differentiate w.r.t. x

$$\frac{2}{x^{2}}$$

Steps Using Definition of a Derivative

Combine x and -x to get 0.

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

Combine -\frac{1}{x} and -\frac{1}{x} to get 2\left(-\frac{1}{x}\right).

$$\frac{\mathrm{d}}{\mathrm{d}x}(2\left(-\frac{1}{x}\right))$$

Express 2\left(-\frac{1}{x}\right) as a single fraction.

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

The derivative of ax^{n} is nax^{n-1}.

$$-\left(-2\right)x^{-1-1}$$

Multiply -1 times -2.

$$2x^{-1-1}$$

Subtract 1 from -1.

$$2x^{-2}$$