Solve 2x/15-3x/20+x/12

$$\frac{ 2x }{ 15 } - \frac{ 3x }{ 20 } + \frac{ x }{ 12 }$$

Evaluate

$$\frac{x}{15}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 15 and 20 is 60. Multiply \frac{2x}{15} times \frac{4}{4}. Multiply \frac{3x}{20} times \frac{3}{3}.

$$\frac{4\times 2x}{60}-\frac{3\times 3x}{60}+\frac{x}{12}$$

Since \frac{4\times 2x}{60} and \frac{3\times 3x}{60} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4\times 2x-3\times 3x}{60}+\frac{x}{12}$$

Do the multiplications in 4\times 2x-3\times 3x.

$$\frac{8x-9x}{60}+\frac{x}{12}$$

Combine like terms in 8x-9x.

$$\frac{-x}{60}+\frac{x}{12}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 60 and 12 is 60. Multiply \frac{x}{12} times \frac{5}{5}.

$$\frac{-x}{60}+\frac{5x}{60}$$

Since \frac{-x}{60} and \frac{5x}{60} have the same denominator, add them by adding their numerators.

$$\frac{-x+5x}{60}$$

Combine like terms in -x+5x.

$$\frac{4x}{60}$$

Divide 4x by 60 to get \frac{1}{15}x.

$$\frac{1}{15}x$$

Differentiate w.r.t. x

$$\frac{1}{15} = 0.06666666666666667$$

Steps Using Definition of a Derivative

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 15 and 20 is 60. Multiply \frac{2x}{15} times \frac{4}{4}. Multiply \frac{3x}{20} times \frac{3}{3}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{4\times 2x}{60}-\frac{3\times 3x}{60}+\frac{x}{12})$$

Since \frac{4\times 2x}{60} and \frac{3\times 3x}{60} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{4\times 2x-3\times 3x}{60}+\frac{x}{12})$$

Do the multiplications in 4\times 2x-3\times 3x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{8x-9x}{60}+\frac{x}{12})$$

Combine like terms in 8x-9x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-x}{60}+\frac{x}{12})$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 60 and 12 is 60. Multiply \frac{x}{12} times \frac{5}{5}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-x}{60}+\frac{5x}{60})$$

Since \frac{-x}{60} and \frac{5x}{60} have the same denominator, add them by adding their numerators.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-x+5x}{60})$$

Combine like terms in -x+5x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{4x}{60})$$

Divide 4x by 60 to get \frac{1}{15}x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{15}x)$$

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

$$\frac{1}{15}x^{1-1}$$

Subtract 1 from 1.

$$\frac{1}{15}x^{0}$$

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

$$\frac{1}{15}\times 1$$

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

$$\frac{1}{15}$$