Solve 6a/8-a/8

$$\frac { 6 a } { 8 } - \frac { a } { 8 }$$

Evaluate

$$\frac{5a}{8}$$

Solution Steps

Divide 6a by 8 to get \frac{3}{4}a.

$$\frac{3}{4}a-\frac{a}{8}$$

Combine \frac{3}{4}a and -\frac{a}{8} to get \frac{5}{8}a.

$$\frac{5}{8}a$$

Differentiate w.r.t. a

$$\frac{5}{8} = 0.625$$

Steps Using Definition of a Derivative

Divide 6a by 8 to get \frac{3}{4}a.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{3}{4}a-\frac{a}{8})$$

Combine \frac{3}{4}a and -\frac{a}{8} to get \frac{5}{8}a.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{5}{8}a)$$

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

$$\frac{5}{8}a^{1-1}$$

Subtract 1 from 1.

$$\frac{5}{8}a^{0}$$

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

$$\frac{5}{8}\times 1$$

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

$$\frac{5}{8}$$