Solve 2x/3-x/6

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

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3 and 6 is 6. Multiply \frac{2x}{3} times \frac{2}{2}.

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

Since \frac{2\times 2x}{6} and \frac{x}{6} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in 2\times 2x-x.

$$\frac{4x-x}{6}$$

Combine like terms in 4x-x.

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

Divide 3x by 6 to get \frac{1}{2}x.

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

Differentiate w.r.t. x

$$\frac{1}{2} = 0.5$$

Steps Using Definition of a Derivative

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3 and 6 is 6. Multiply \frac{2x}{3} times \frac{2}{2}.

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

Since \frac{2\times 2x}{6} and \frac{x}{6} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in 2\times 2x-x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{4x-x}{6})$$

Combine like terms in 4x-x.

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

Divide 3x by 6 to get \frac{1}{2}x.

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

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

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

Subtract 1 from 1.

$$\frac{1}{2}x^{0}$$

For any term t except 0, t^{0}=1.

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

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

$$\frac{1}{2}$$