Solve 1/2a+1/3a-2/3a+5/2a

$$\frac { 1 } { 2 } a + \frac { 1 } { 3 } a - \frac { 2 } { 3 } a + \frac { 5 } { 2 } a$$

Evaluate

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

Solution Steps

Combine \frac{1}{2}a and \frac{1}{3}a to get \frac{5}{6}a.

$$\frac{5}{6}a-\frac{2}{3}a+\frac{5}{2}a$$

Combine \frac{5}{6}a and -\frac{2}{3}a to get \frac{1}{6}a.

$$\frac{1}{6}a+\frac{5}{2}a$$

Combine \frac{1}{6}a and \frac{5}{2}a to get \frac{8}{3}a.

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

Differentiate w.r.t. a

$$\frac{8}{3} = 2\frac{2}{3} = 2.6666666666666665$$

Steps Using Definition of a Derivative

Combine \frac{1}{2}a and \frac{1}{3}a to get \frac{5}{6}a.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{5}{6}a-\frac{2}{3}a+\frac{5}{2}a)$$

Combine \frac{5}{6}a and -\frac{2}{3}a to get \frac{1}{6}a.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{1}{6}a+\frac{5}{2}a)$$

Combine \frac{1}{6}a and \frac{5}{2}a to get \frac{8}{3}a.

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

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

$$\frac{8}{3}a^{1-1}$$

Subtract 1 from 1.

$$\frac{8}{3}a^{0}$$

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

$$\frac{8}{3}\times 1$$

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

$$\frac{8}{3}$$