Solve (2/x)3

$$( \frac{ 2 }{ x } )3$$

Evaluate

$$\frac{6}{x}$$

Solution Steps

Express \frac{2}{x}\times 3 as a single fraction.

$$\frac{2\times 3}{x}$$

Multiply 2 and 3 to get 6.

$$\frac{6}{x}$$

Differentiate w.r.t. x

$$-\frac{6}{x^{2}}$$

Steps Using Definition of a Derivative

Express \frac{2}{x}\times 3 as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2\times 3}{x})$$

Multiply 2 and 3 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{6}{x})$$

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

$$-6x^{-1-1}$$

Subtract 1 from -1.

$$-6x^{-2}$$