Solve 1/2a-1/3a-1/4a=

$$\frac { 1 } { 2 } a - \frac { 1 } { 3 } a - \frac { 1 } { 4 } a =$$

Evaluate

$$-\frac{a}{12}$$

Solution Steps

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

$$\frac{1}{6}a-\frac{1}{4}a$$

Combine \frac{1}{6}a and -\frac{1}{4}a to get -\frac{1}{12}a.

$$-\frac{1}{12}a$$

Differentiate w.r.t. a

$$-\frac{1}{12} = -0.08333333333333333$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{1}{6}a-\frac{1}{4}a)$$

Combine \frac{1}{6}a and -\frac{1}{4}a to get -\frac{1}{12}a.

$$\frac{\mathrm{d}}{\mathrm{d}a}(-\frac{1}{12}a)$$

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

$$-\frac{1}{12}a^{1-1}$$

Subtract 1 from 1.

$$-\frac{1}{12}a^{0}$$

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

$$-\frac{1}{12}$$