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

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

Evaluate

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

Solution Steps

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

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

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

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

Differentiate w.r.t. a

$$-\frac{1}{6} = -0.16666666666666666$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{1}{2}a-\frac{2}{3}a)$$

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(-\frac{1}{6}a)$$

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

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

Subtract 1 from 1.

$$-\frac{1}{6}a^{0}$$

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

$$-\frac{1}{6}$$