Solve (frac{2/xfrac{{}}}{}

$$( \frac{ \frac{ 2 }{ x \frac{ }{ } } }{ }$$

Evaluate

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

Solution Steps

Divide 1 by 1 to get 1.

$$\frac{\frac{2}{x\times 1}}{1}$$

Anything divided by one gives itself.

$$\frac{2}{x\times 1}$$

For any term t, t\times 1=t and 1t=t.

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

Differentiate w.r.t. x

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

Steps Using Definition of a Derivative

Divide 1 by 1 to get 1.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\frac{2}{x\times 1}}{1})$$

Anything divided by one gives itself.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2}{x\times 1})$$

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

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

Subtract 1 from -1.

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