Solve (x+1)+(x-1/2-1x-1/2)]+3

$$( x + 1 ) + ( x - \frac { 1 } { 2 } - 1 x - \frac { 1 } { 2 } ) ] + 3$$

Evaluate

$$x$$

Solution Steps

Combine x and x to get 2x.

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

Convert 1 to fraction \frac{2}{2}.

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

Since \frac{2}{2} and \frac{1}{2} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 1 from 2 to get 1.

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

Combine 2x and -x to get x.

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

Subtract \frac{1}{2} from \frac{1}{2} to get 0.

$$x$$

Differentiate w.r.t. x

$$1$$

Steps Using Definition of a Derivative

Combine x and x to get 2x.

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

Convert 1 to fraction \frac{2}{2}.

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

Since \frac{2}{2} and \frac{1}{2} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 1 from 2 to get 1.

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

Combine 2x and -x to get x.

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

Subtract \frac{1}{2} from \frac{1}{2} to get 0.

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

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.

$$1$$