Solve 1+x/sqrt{2}

$$\frac { 1 + x } { \sqrt { 2 } }$$

Evaluate

$$\frac{\sqrt{2}\left(x+1\right)}{2}$$

Solution Steps

Rationalize the denominator of \frac{1+x}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{\left(1+x\right)\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{\left(1+x\right)\sqrt{2}}{2}$$

Use the distributive property to multiply 1+x by \sqrt{2}.

$$\frac{\sqrt{2}+x\sqrt{2}}{2}$$

Differentiate w.r.t. x

$$\frac{\sqrt{2}}{2} = 0.7071067811865476$$