Solve 5x-(-x)+(x)-(-3x)+(-2x)=

$$5 x - ( - x ) + ( x ) - ( - 3 x ) + ( - 2 x ) =$$

Evaluate

$$8x$$

Solution Steps

The opposite of -3x is 3x.

$$5x-\left(-x\right)+x+3x-2x$$

Combine x and 3x to get 4x.

$$5x-\left(-x\right)+4x-2x$$

Combine 4x and -2x to get 2x.

$$5x-\left(-x\right)+2x$$

Multiply -1 and -1 to get 1.

$$5x+x+2x$$

Combine 5x and x to get 6x.

$$6x+2x$$

Combine 6x and 2x to get 8x.

$$8x$$

Differentiate w.r.t. x

$$8$$

Steps Using Definition of a Derivative

The opposite of -3x is 3x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(5x-\left(-x\right)+x+3x-2x)$$

Combine x and 3x to get 4x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(5x-\left(-x\right)+4x-2x)$$

Combine 4x and -2x to get 2x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(5x-\left(-x\right)+2x)$$

Multiply -1 and -1 to get 1.

$$\frac{\mathrm{d}}{\mathrm{d}x}(5x+x+2x)$$

Combine 5x and x to get 6x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(6x+2x)$$

Combine 6x and 2x to get 8x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(8x)$$

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

$$8x^{1-1}$$

Subtract 1 from 1.

$$8x^{0}$$

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

$$8\times 1$$

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

$$8$$