Solve 3x/3-2x2/2

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

Evaluate

$$-x$$

Solution Steps

Divide 2 by 2 to get 1.

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

Cancel out 3 and 3.

$$x-2x\times 1$$

Multiply 2 and 1 to get 2.

$$x-2x$$

Combine x and -2x to get -x.

$$-x$$

Differentiate w.r.t. x

$$-1$$

Steps Using Definition of a Derivative

Divide 2 by 2 to get 1.

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

Cancel out 3 and 3.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x-2x\times 1)$$

Multiply 2 and 1 to get 2.

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

Combine x and -2x to get -x.

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

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

$$-x^{1-1}$$

Subtract 1 from 1.

$$-x^{0}$$

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

$$-1$$