Solve a-1/2a+1/5a

$$a - \frac { 1 } { 2 } a + \frac { 1 } { 5 } a$$

Evaluate

$$\frac{7a}{10}$$

Solution Steps

Combine a and -\frac{1}{2}a to get \frac{1}{2}a.

$$\frac{1}{2}a+\frac{1}{5}a$$

Combine \frac{1}{2}a and \frac{1}{5}a to get \frac{7}{10}a.

$$\frac{7}{10}a$$

Differentiate w.r.t. a

$$\frac{7}{10} = 0.7$$

Steps Using Definition of a Derivative

Combine a and -\frac{1}{2}a to get \frac{1}{2}a.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{1}{2}a+\frac{1}{5}a)$$

Combine \frac{1}{2}a and \frac{1}{5}a to get \frac{7}{10}a.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{7}{10}a)$$

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

$$\frac{7}{10}a^{1-1}$$

Subtract 1 from 1.

$$\frac{7}{10}a^{0}$$

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

$$\frac{7}{10}\times 1$$

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

$$\frac{7}{10}$$