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

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

Evaluate

$$x$$

Solution Steps

Use the distributive property to multiply 1 by \frac{1}{2}x+\frac{1}{3}y.

$$\frac{1}{2}x+\frac{1}{3}y+\frac{1}{2}x-\frac{1}{3}y$$

Combine \frac{1}{2}x and \frac{1}{2}x to get x.

$$x+\frac{1}{3}y-\frac{1}{3}y$$

Combine \frac{1}{3}y and -\frac{1}{3}y to get 0.

$$x$$

Differentiate w.r.t. x

$$1$$

Steps Using Definition of a Derivative

Use the distributive property to multiply 1 by \frac{1}{2}x+\frac{1}{3}y.

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

Combine \frac{1}{2}x and \frac{1}{2}x to get x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x+\frac{1}{3}y-\frac{1}{3}y)$$

Combine \frac{1}{3}y and -\frac{1}{3}y 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.

$$1$$