Solve 5x/6-2x/3

$$\frac { 5 x } { 6 } - \frac { 2 x } { 3 }$$

Evaluate

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

Short Solution Steps

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

$$\frac{5x}{6}-\frac{2\times 2x}{6}$$

Since \frac{5x}{6} and \frac{2\times 2x}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5x-2\times 2x}{6}$$

Do the multiplications in 5x-2\times 2x.

$$\frac{5x-4x}{6}$$

Combine like terms in 5x-4x.

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

Differentiate w.r.t. x

$$\frac{1}{6} = 0.16666666666666666$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5x}{6}-\frac{2\times 2x}{6})$$

Since \frac{5x}{6} and \frac{2\times 2x}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5x-2\times 2x}{6})$$

Do the multiplications in 5x-2\times 2x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5x-4x}{6})$$

Combine like terms in 5x-4x.

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

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

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

Subtract 1 from 1.

$$\frac{1}{6}x^{0}$$

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

$$\frac{1}{6}\times 1$$

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

$$\frac{1}{6}$$