Solve (x^2+4x+2-x+2)

$$( x ^ { 2 } + 4 x + 2 - x + 2 )$$

Evaluate

$$x^{2}+3x+4$$

Solution Steps

Combine 4x and -x to get 3x.

$$x^{2}+3x+2+2$$

Add 2 and 2 to get 4.

$$x^{2}+3x+4$$

Differentiate w.r.t. x

$$2x+3$$

Steps Using Derivative Rule for Sum

Combine 4x and -x to get 3x.

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

Add 2 and 2 to get 4.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}+3x+4)$$

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}.

$$2x^{2-1}+3x^{1-1}$$

Subtract 1 from 2.

$$2x^{1}+3x^{1-1}$$

Subtract 1 from 1.

$$2x^{1}+3x^{0}$$

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

$$2x+3x^{0}$$

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

$$2x+3\times 1$$

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

$$2x+3$$