Solve frac{2sqrt{2}x}{frac{sqrt{3}}{2}}

$$\frac { 2 \sqrt { 2 } x } { \frac { \sqrt { 3 } } { 2 } }$$

Evaluate

$$\frac{4\sqrt{6}x}{3}$$

Solution Steps

Divide 2\sqrt{2}x by \frac{\sqrt{3}}{2} by multiplying 2\sqrt{2}x by the reciprocal of \frac{\sqrt{3}}{2}.

$$\frac{2\sqrt{2}x\times 2}{\sqrt{3}}$$

Multiply 2 and 2 to get 4.

$$\frac{4\sqrt{2}x}{\sqrt{3}}$$

Rationalize the denominator of \frac{4\sqrt{2}x}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{4\sqrt{2}x\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{4\sqrt{2}x\sqrt{3}}{3}$$

To multiply \sqrt{2} and \sqrt{3}, multiply the numbers under the square root.

$$\frac{4\sqrt{6}x}{3}$$

Differentiate w.r.t. x

$$\frac{4 \sqrt{6}}{3} = 3.2659863237109037$$