Solve -4n/6+3n/6

$$- \frac { 4 n } { 6 } + \frac { 3 n } { 6 }$$

Evaluate

$$-\frac{n}{6}$$

Solution Steps

Divide 4n by 6 to get \frac{2}{3}n.

$$-\frac{2}{3}n+\frac{3n}{6}$$

Divide 3n by 6 to get \frac{1}{2}n.

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

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

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

Differentiate w.r.t. n

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

Steps Using Definition of a Derivative

Divide 4n by 6 to get \frac{2}{3}n.

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

Divide 3n by 6 to get \frac{1}{2}n.

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

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

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

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

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

Subtract 1 from 1.

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

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

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