Solve 2/3x/frac{1{6}}

$$\frac { \frac { 2 } { 3 x } } { \frac { 1 } { 6 } }$$

Evaluate

$$\frac{4}{x}$$

Solution Steps

Divide \frac{2}{3x} by \frac{1}{6} by multiplying \frac{2}{3x} by the reciprocal of \frac{1}{6}.

$$\frac{2\times 6}{3x}$$

Cancel out 3 in both numerator and denominator.

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

Multiply 2 and 2 to get 4.

$$\frac{4}{x}$$

Differentiate w.r.t. x

$$-\frac{4}{x^{2}}$$

Steps Using Definition of a Derivative

Divide \frac{2}{3x} by \frac{1}{6} by multiplying \frac{2}{3x} by the reciprocal of \frac{1}{6}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2\times 6}{3x})$$

Cancel out 3 in both numerator and denominator.

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

Multiply 2 and 2 to get 4.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{4}{x})$$

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

$$-4x^{-1-1}$$

Subtract 1 from -1.

$$-4x^{-2}$$