Solve {l}{x^2-(sqrt{2}-1)}{+sqrt{2}}

$$\left. \begin{array} { l } { x ^ { 2 } - ( \sqrt { 2 } - 1 ) } \\ { + \sqrt { 2 } } \end{array} \right.$$

Evaluate

$$x^{2}+1$$

Solution Steps

To find the opposite of \sqrt{2}-1, find the opposite of each term.

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

Combine -\sqrt{2} and \sqrt{2} to get 0.

$$x^{2}+1$$

Differentiate w.r.t. x

$$2x$$

Steps Using Derivative Rule for Sum

To find the opposite of \sqrt{2}-1, find the opposite of each term.

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

Combine -\sqrt{2} and \sqrt{2} to get 0.

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

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}.

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

Subtract 1 from 2.

$$2x^{1}$$

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

$$2x$$