Solve 12x/15-10/15x

$$\frac { 12 x } { 15 } - \frac { 10 } { 15 } x$$

Evaluate

$$\frac{2x}{15}$$

Solution Steps

Divide 12x by 15 to get \frac{4}{5}x.

$$\frac{4}{5}x-\frac{10}{15}x$$

Reduce the fraction \frac{10}{15} to lowest terms by extracting and canceling out 5.

$$\frac{4}{5}x-\frac{2}{3}x$$

Combine \frac{4}{5}x and -\frac{2}{3}x to get \frac{2}{15}x.

$$\frac{2}{15}x$$

Differentiate w.r.t. x

$$\frac{2}{15} = 0.13333333333333333$$

Steps Using Definition of a Derivative

Divide 12x by 15 to get \frac{4}{5}x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{4}{5}x-\frac{10}{15}x)$$

Reduce the fraction \frac{10}{15} to lowest terms by extracting and canceling out 5.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{4}{5}x-\frac{2}{3}x)$$

Combine \frac{4}{5}x and -\frac{2}{3}x to get \frac{2}{15}x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2}{15}x)$$

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

$$\frac{2}{15}x^{1-1}$$

Subtract 1 from 1.

$$\frac{2}{15}x^{0}$$

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

$$\frac{2}{15}\times 1$$

For any term t, t\times 1=t and 1t=t.

$$\frac{2}{15}$$