Solve 8x-2x-4x+x=

$$8 x - 2 x - 4 x + x =$$

Evaluate

$$3x$$

Solution Steps

Combine 8x and -2x to get 6x.

$$6x-4x+x$$

Combine 6x and -4x to get 2x.

$$2x+x$$

Combine 2x and x to get 3x.

$$3x$$

Differentiate w.r.t. x

$$3$$

Steps Using Definition of a Derivative

Combine 8x and -2x to get 6x.

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

Combine 6x and -4x to get 2x.

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

Combine 2x and x to get 3x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(3x)$$

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

$$3x^{1-1}$$

Subtract 1 from 1.

$$3x^{0}$$

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

$$3\times 1$$

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

$$3$$