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

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

Evaluate

$$y$$

Solution Steps

Use the distributive property to multiply 3 by 2x-y.

$$6x-3y-2\left(3x-2y\right)$$

Use the distributive property to multiply -2 by 3x-2y.

$$6x-3y-6x+4y$$

Combine 6x and -6x to get 0.

$$-3y+4y$$

Combine -3y and 4y to get y.

$$y$$

Differentiate w.r.t. y

$$1$$

Steps Using Definition of a Derivative

Use the distributive property to multiply 3 by 2x-y.

$$\frac{\mathrm{d}}{\mathrm{d}y}(6x-3y-2\left(3x-2y\right))$$

Use the distributive property to multiply -2 by 3x-2y.

$$\frac{\mathrm{d}}{\mathrm{d}y}(6x-3y-6x+4y)$$

Combine 6x and -6x to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}y}(-3y+4y)$$

Combine -3y and 4y to get y.

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

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

$$y^{1-1}$$

Subtract 1 from 1.

$$y^{0}$$

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

$$1$$