Solve 7d/9-19d/36=

$$\frac { 7 d } { 9 } - \frac { 19 d } { 36 } =$$

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 9 and 36 is 36. Multiply \frac{7d}{9} times \frac{4}{4}.

$$\frac{4\times 7d}{36}-\frac{19d}{36}$$

Since \frac{4\times 7d}{36} and \frac{19d}{36} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4\times 7d-19d}{36}$$

Do the multiplications in 4\times 7d-19d.

$$\frac{28d-19d}{36}$$

Combine like terms in 28d-19d.

$$\frac{9d}{36}$$

Divide 9d by 36 to get \frac{1}{4}d.

$$\frac{1}{4}d$$

Differentiate w.r.t. d

$$\frac{1}{4} = 0.25$$

Steps Using Definition of a Derivative

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 9 and 36 is 36. Multiply \frac{7d}{9} times \frac{4}{4}.

$$\frac{\mathrm{d}}{\mathrm{d}d}(\frac{4\times 7d}{36}-\frac{19d}{36})$$

Since \frac{4\times 7d}{36} and \frac{19d}{36} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\mathrm{d}}{\mathrm{d}d}(\frac{4\times 7d-19d}{36})$$

Do the multiplications in 4\times 7d-19d.

$$\frac{\mathrm{d}}{\mathrm{d}d}(\frac{28d-19d}{36})$$

Combine like terms in 28d-19d.

$$\frac{\mathrm{d}}{\mathrm{d}d}(\frac{9d}{36})$$

Divide 9d by 36 to get \frac{1}{4}d.

$$\frac{\mathrm{d}}{\mathrm{d}d}(\frac{1}{4}d)$$

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

$$\frac{1}{4}d^{1-1}$$

Subtract 1 from 1.

$$\frac{1}{4}d^{0}$$

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

$$\frac{1}{4}\times 1$$

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

$$\frac{1}{4}$$