Solve 3d/4-5d/12

$$\frac{ 3d }{ 4 } - \frac{ 5d }{ 12 }$$

Evaluate

$$\frac{d}{3}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4 and 12 is 12. Multiply \frac{3d}{4} times \frac{3}{3}.

$$\frac{3\times 3d}{12}-\frac{5d}{12}$$

Since \frac{3\times 3d}{12} and \frac{5d}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3\times 3d-5d}{12}$$

Do the multiplications in 3\times 3d-5d.

$$\frac{9d-5d}{12}$$

Combine like terms in 9d-5d.

$$\frac{4d}{12}$$

Divide 4d by 12 to get \frac{1}{3}d.

$$\frac{1}{3}d$$

Differentiate w.r.t. d

$$\frac{1}{3} = 0.3333333333333333$$

Steps Using Definition of a Derivative

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4 and 12 is 12. Multiply \frac{3d}{4} times \frac{3}{3}.

$$\frac{\mathrm{d}}{\mathrm{d}d}(\frac{3\times 3d}{12}-\frac{5d}{12})$$

Since \frac{3\times 3d}{12} and \frac{5d}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\mathrm{d}}{\mathrm{d}d}(\frac{3\times 3d-5d}{12})$$

Do the multiplications in 3\times 3d-5d.

$$\frac{\mathrm{d}}{\mathrm{d}d}(\frac{9d-5d}{12})$$

Combine like terms in 9d-5d.

$$\frac{\mathrm{d}}{\mathrm{d}d}(\frac{4d}{12})$$

Divide 4d by 12 to get \frac{1}{3}d.

$$\frac{\mathrm{d}}{\mathrm{d}d}(\frac{1}{3}d)$$

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

$$\frac{1}{3}d^{1-1}$$

Subtract 1 from 1.

$$\frac{1}{3}d^{0}$$

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

$$\frac{1}{3}\times 1$$

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

$$\frac{1}{3}$$