Solve 1-a/sqrt{2}

$$\frac { 1 - a } { \sqrt { 2 } }$$

Evaluate

$$\frac{\sqrt{2}\left(1-a\right)}{2}$$

Solution Steps

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

$$\frac{\left(1-a\right)\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{\left(1-a\right)\sqrt{2}}{2}$$

Use the distributive property to multiply 1-a by \sqrt{2}.

$$\frac{\sqrt{2}-a\sqrt{2}}{2}$$

Differentiate w.r.t. a

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