Solve x+2x+2x+x=

$$x + 2 x + 2 x + x =$$

Evaluate

$$6x$$

Solution Steps

Combine x and 2x to get 3x.

$$3x+2x+x$$

Combine 3x and 2x to get 5x.

$$5x+x$$

Combine 5x and x to get 6x.

$$6x$$

Differentiate w.r.t. x

$$6$$

Steps Using Definition of a Derivative

Combine x and 2x to get 3x.

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

Combine 3x and 2x to get 5x.

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

Combine 5x and x to get 6x.

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

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

$$6x^{1-1}$$

Subtract 1 from 1.

$$6x^{0}$$

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

$$6\times 1$$

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

$$6$$