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

$$( 3 x + y ) - ( 2 x + y )$$

Evaluate

$$x$$

Solution Steps

To find the opposite of 2x+y, find the opposite of each term.

$$3x+y-2x-y$$

Combine 3x and -2x to get x.

$$x+y-y$$

Combine y and -y to get 0.

$$x$$

Differentiate w.r.t. x

$$1$$

Steps Using Definition of a Derivative

To find the opposite of 2x+y, find the opposite of each term.

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

Combine 3x and -2x to get x.

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

Combine y and -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.

$$1$$