Solve (2x-2)+(x+1)+x+(x+1)

$$( 2 x - 2 ) + ( x + 1 ) + x + ( x + 1 )$$

Evaluate

$$5x$$

Solution Steps

Combine 2x and x to get 3x.

$$3x-2+1+x+x+1$$

Add -2 and 1 to get -1.

$$3x-1+x+x+1$$

Combine 3x and x to get 4x.

$$4x-1+x+1$$

Combine 4x and x to get 5x.

$$5x-1+1$$

Add -1 and 1 to get 0.

$$5x$$

Differentiate w.r.t. x

$$5$$

Steps Using Definition of a Derivative

Combine 2x and x to get 3x.

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

Add -2 and 1 to get -1.

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

Combine 3x and x to get 4x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(4x-1+x+1)$$

Combine 4x and x to get 5x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(5x-1+1)$$

Add -1 and 1 to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}x}(5x)$$

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

$$5x^{1-1}$$

Subtract 1 from 1.

$$5x^{0}$$

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

$$5\times 1$$

For any term t, t\times 1=t and 1t=t.

$$5$$