Solve 18/frac{x{3}}

$$\frac { 18 } { \frac { x } { 3 } }$$

Evaluate

$$\frac{54}{x}$$

Solution Steps

Divide 18 by \frac{x}{3} by multiplying 18 by the reciprocal of \frac{x}{3}.

$$\frac{18\times 3}{x}$$

Multiply 18 and 3 to get 54.

$$\frac{54}{x}$$

Differentiate w.r.t. x

$$-\frac{54}{x^{2}}$$

Steps Using Definition of a Derivative

Divide 18 by \frac{x}{3} by multiplying 18 by the reciprocal of \frac{x}{3}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{18\times 3}{x})$$

Multiply 18 and 3 to get 54.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{54}{x})$$

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

$$-54x^{-1-1}$$

Subtract 1 from -1.

$$-54x^{-2}$$