Solve 3x-2x+3x-2x=

$$3 x - 2 x + 3 x - 2 x =$$

Evaluate

$$2x$$

Solution Steps

Combine 3x and -2x to get x.

$$x+3x-2x$$

Combine x and 3x to get 4x.

$$4x-2x$$

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

$$2x$$

Differentiate w.r.t. x

$$2$$

Steps Using Definition of a Derivative

Combine 3x and -2x to get x.

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

Combine x and 3x to get 4x.

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

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

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

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

$$2x^{1-1}$$

Subtract 1 from 1.

$$2x^{0}$$

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

$$2\times 1$$

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

$$2$$