Solve x^2+x+x+-x+1

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

Evaluate

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

Solution Steps

Combine x and x to get 2x.

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

Combine 2x and -x to get x.

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

Differentiate w.r.t. x

$$2x+1$$

Steps Using Derivative Rule for Sum

Combine x and x to get 2x.

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

Combine 2x and -x to get x.

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

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}.

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

Subtract 1 from 2.

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

Subtract 1 from 1.

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

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

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

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

$$2x+1$$