Solve a+1/2a+2/3a

$$a + \frac { 1 } { 2 } a + \frac { 2 } { 3 } a$$

Evaluate

$$\frac{13a}{6}$$

Solution Steps

Combine a and \frac{1}{2}a to get \frac{3}{2}a.

$$\frac{3}{2}a+\frac{2}{3}a$$

Combine \frac{3}{2}a and \frac{2}{3}a to get \frac{13}{6}a.

$$\frac{13}{6}a$$

Differentiate w.r.t. a

$$\frac{13}{6} = 2\frac{1}{6} = 2.1666666666666665$$

Steps Using Definition of a Derivative

Combine a and \frac{1}{2}a to get \frac{3}{2}a.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{3}{2}a+\frac{2}{3}a)$$

Combine \frac{3}{2}a and \frac{2}{3}a to get \frac{13}{6}a.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{13}{6}a)$$

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

$$\frac{13}{6}a^{1-1}$$

Subtract 1 from 1.

$$\frac{13}{6}a^{0}$$

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

$$\frac{13}{6}\times 1$$

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

$$\frac{13}{6}$$