Solve -8x/12-9x/12

$$\frac{ -8x }{ 12 } - \frac{ 9x }{ 12 }$$

Evaluate

$$-\frac{17x}{12}$$

Solution Steps

Divide -8x by 12 to get -\frac{2}{3}x.

$$-\frac{2}{3}x-\frac{9x}{12}$$

Divide 9x by 12 to get \frac{3}{4}x.

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

Combine -\frac{2}{3}x and -\frac{3}{4}x to get -\frac{17}{12}x.

$$-\frac{17}{12}x$$

Differentiate w.r.t. x

$$-\frac{17}{12} = -1\frac{5}{12} = -1.4166666666666667$$

Steps Using Definition of a Derivative

Divide -8x by 12 to get -\frac{2}{3}x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-\frac{2}{3}x-\frac{9x}{12})$$

Divide 9x by 12 to get \frac{3}{4}x.

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

Combine -\frac{2}{3}x and -\frac{3}{4}x to get -\frac{17}{12}x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-\frac{17}{12}x)$$

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

$$-\frac{17}{12}x^{1-1}$$

Subtract 1 from 1.

$$-\frac{17}{12}x^{0}$$

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

$$-\frac{17}{12}$$