Solve -8x/6+3x/6+3x/6

$$- \frac { 8 x } { 6 } + \frac { 3 x } { 6 } + \frac { 3 x } { 6 }$$

Evaluate

$$-\frac{x}{3}$$

Solution Steps

Divide 8x by 6 to get \frac{4}{3}x.

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

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

$$-\frac{4}{3}x+\frac{1}{2}x+\frac{3x}{6}$$

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

$$-\frac{4}{3}x+\frac{1}{2}x+\frac{1}{2}x$$

Combine \frac{1}{2}x and \frac{1}{2}x to get x.

$$-\frac{4}{3}x+x$$

Combine -\frac{4}{3}x and x to get -\frac{1}{3}x.

$$-\frac{1}{3}x$$

Differentiate w.r.t. x

$$-\frac{1}{3} = -0.3333333333333333$$

Steps Using Definition of a Derivative

Divide 8x by 6 to get \frac{4}{3}x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-\frac{4}{3}x+\frac{3x}{6}+\frac{3x}{6})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(-\frac{4}{3}x+\frac{1}{2}x+\frac{3x}{6})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(-\frac{4}{3}x+\frac{1}{2}x+\frac{1}{2}x)$$

Combine \frac{1}{2}x and \frac{1}{2}x to get x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-\frac{4}{3}x+x)$$

Combine -\frac{4}{3}x and x to get -\frac{1}{3}x.

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

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

$$-\frac{1}{3}x^{1-1}$$

Subtract 1 from 1.

$$-\frac{1}{3}x^{0}$$

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

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