Solve d/2/sqrt{6/3C}

$$\frac { \frac { d } { 2 } } { \frac { \sqrt { 6 } } { 3 } C }$$

Evaluate

$$\frac{\sqrt{6}d}{4C}$$

Short Solution Steps

Express \frac{\frac{d}{2}}{\frac{\sqrt{6}}{3}C} as a single fraction.

$$\frac{d}{2\times \frac{\sqrt{6}}{3}C}$$

Express 2\times \frac{\sqrt{6}}{3} as a single fraction.

$$\frac{d}{\frac{2\sqrt{6}}{3}C}$$

Express \frac{2\sqrt{6}}{3}C as a single fraction.

$$\frac{d}{\frac{2\sqrt{6}C}{3}}$$

Divide d by \frac{2\sqrt{6}C}{3} by multiplying d by the reciprocal of \frac{2\sqrt{6}C}{3}.

$$\frac{d\times 3}{2\sqrt{6}C}$$

Rationalize the denominator of \frac{d\times 3}{2\sqrt{6}C} by multiplying numerator and denominator by \sqrt{6}.

$$\frac{d\times 3\sqrt{6}}{2\left(\sqrt{6}\right)^{2}C}$$

The square of \sqrt{6} is 6.

$$\frac{d\times 3\sqrt{6}}{2\times 6C}$$

Multiply 2 and 6 to get 12.

$$\frac{d\times 3\sqrt{6}}{12C}$$

Cancel out 3 in both numerator and denominator.

$$\frac{\sqrt{6}d}{4C}$$

Differentiate w.r.t. d

$$\frac{\sqrt{6}}{4C}$$