Solve (x)+(x+1)+(x+3)

$$( x ) + ( x + 1 ) + ( x + 3 )$$

Evaluate

$$3x+4$$

Solution Steps

Combine x and x to get 2x.

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

Combine 2x and x to get 3x.

$$3x+1+3$$

Add 1 and 3 to get 4.

$$3x+4$$

Differentiate w.r.t. x

$$3$$

Steps Using Derivative Rule for Sum

Combine x and x to get 2x.

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

Combine 2x and x to get 3x.

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

Add 1 and 3 to get 4.

$$\frac{\mathrm{d}}{\mathrm{d}x}(3x+4)$$

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. 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.

$$3$$