Solve 6/2*x/3-x/3

$$\frac { 6 } { 2 } \cdot \frac { x } { 3 } - \frac { x } { 3 }$$

Evaluate

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

Solution Steps

Divide 6 by 2 to get 3.

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

Cancel out 3 and 3.

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

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

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

Differentiate w.r.t. x

$$\frac{2}{3} = 0.6666666666666666$$

Steps Using Definition of a Derivative

Divide 6 by 2 to get 3.

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

Cancel out 3 and 3.

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

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

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

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

$$\frac{2}{3}x^{1-1}$$

Subtract 1 from 1.

$$\frac{2}{3}x^{0}$$

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

$$\frac{2}{3}\times 1$$

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

$$\frac{2}{3}$$