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

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

Evaluate

$$\frac{x}{2}$$

Solution Steps

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

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

The square of \sqrt{3} is 3.

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

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

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

Multiply 2 and 3 to get 6.

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

Reduce the fraction \frac{3}{6} to lowest terms by extracting and canceling out 3.

$$\frac{1}{2}x$$

Differentiate w.r.t. x

$$\frac{1}{2} = 0.5$$

Steps Using Definition of a Derivative

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

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

The square of \sqrt{3} is 3.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\sqrt{3}\sqrt{3}}{2\times 3}x)$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3}{2\times 3}x)$$

Multiply 2 and 3 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3}{6}x)$$

Reduce the fraction \frac{3}{6} to lowest terms by extracting and canceling out 3.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{2}x)$$

The derivative of ax^{n} is nax^{n-1}.

$$\frac{1}{2}x^{1-1}$$

Subtract 1 from 1.

$$\frac{1}{2}x^{0}$$

For any term t except 0, t^{0}=1.

$$\frac{1}{2}\times 1$$

For any term t, t\times 1=t and 1t=t.

$$\frac{1}{2}$$