Solve 1/2(2x-4y)+2y

$$\frac{ 1 }{ 2 } (2x-4y)+2y$$

Evaluate

$$x$$

Solution Steps

Use the distributive property to multiply \frac{1}{2} by 2x-4y.

$$\frac{1}{2}\times 2x+\frac{1}{2}\left(-4\right)y+2y$$

Cancel out 2 and 2.

$$x+\frac{1}{2}\left(-4\right)y+2y$$

Multiply \frac{1}{2} and -4 to get \frac{-4}{2}.

$$x+\frac{-4}{2}y+2y$$

Divide -4 by 2 to get -2.

$$x-2y+2y$$

Combine -2y and 2y to get 0.

$$x$$

Differentiate w.r.t. x

$$1$$

Steps Using Definition of a Derivative

Use the distributive property to multiply \frac{1}{2} by 2x-4y.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{2}\times 2x+\frac{1}{2}\left(-4\right)y+2y)$$

Cancel out 2 and 2.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x+\frac{1}{2}\left(-4\right)y+2y)$$

Multiply \frac{1}{2} and -4 to get \frac{-4}{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x+\frac{-4}{2}y+2y)$$

Divide -4 by 2 to get -2.

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

Combine -2y and 2y 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.

$$1$$