Solve x^2/x^1sqrt{2}+frac{sqrt[2]{4}}{sqrt{2}}

$$\frac { x ^ { 2 } } { x ^ { 1 } \sqrt { 2 } } + \frac { \sqrt[ 2 ] { 4 } } { \sqrt { 2 } }$$

Evaluate

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

Short Solution Steps

Cancel out x in both numerator and denominator.

$$\frac{x}{\sqrt{2}}+\frac{\sqrt[2]{4}}{\sqrt{2}}$$

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

$$\frac{x\sqrt{2}}{\left(\sqrt{2}\right)^{2}}+\frac{\sqrt[2]{4}}{\sqrt{2}}$$

The square of \sqrt{2} is 2.

$$\frac{x\sqrt{2}}{2}+\frac{\sqrt[2]{4}}{\sqrt{2}}$$

Calculate \sqrt[2]{4} and get 2.

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

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

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

The square of \sqrt{2} is 2.

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

Since \frac{x\sqrt{2}}{2} and \frac{2\sqrt{2}}{2} have the same denominator, add them by adding their numerators.

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

Differentiate w.r.t. x

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