Solve x^2+1+2x-2+3

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

Evaluate

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

Solution Steps

Subtract 2 from 1 to get -1.

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

Add -1 and 3 to get 2.

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

Differentiate w.r.t. x

$$2\left(x+1\right)$$

Steps Using Derivative Rule for Sum

Subtract 2 from 1 to get -1.

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

Add -1 and 3 to get 2.

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

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}.

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

Subtract 1 from 2.

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

Subtract 1 from 1.

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

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

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

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

$$2x+2\times 1$$

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

$$2x+2$$