Solve frac{sqrt{3}}{2}x^2quadtext{(c)}x^2/sqrt{3}

$$\frac { \sqrt { 3 } } { 2 } x ^ { 2 } \quad \text { (c) } \frac { x ^ { 2 } } { \sqrt { 3 } }$$

Evaluate

$$\frac{cx^{4}}{2}$$

Solution Steps

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

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

The square of \sqrt{3} is 3.

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

Express \frac{\sqrt{3}}{2}x^{2} as a single fraction.

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

Express \frac{\sqrt{3}x^{2}}{2}c as a single fraction.

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

Multiply \frac{\sqrt{3}x^{2}c}{2} times \frac{x^{2}\sqrt{3}}{3} by multiplying numerator times numerator and denominator times denominator.

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

Multiply \sqrt{3} and \sqrt{3} to get 3.

$$\frac{3x^{2}cx^{2}}{2\times 3}$$

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$\frac{3x^{4}c}{2\times 3}$$

Cancel out 3 in both numerator and denominator.

$$\frac{cx^{4}}{2}$$

Differentiate w.r.t. x

$$2cx^{3}$$