Solve sqrt{3}xfrac{sqrt{3}}{3}

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

Evaluate

$$x$$

Solution Steps

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

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

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

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

Divide 3 by 3 to get 1.

$$1x$$

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

$$x$$

Differentiate w.r.t. x

$$1$$

Steps Using Definition of a Derivative

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

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

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

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

Divide 3 by 3 to get 1.

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

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

$$x^{1-1}$$

Subtract 1 from 1.

$$x^{0}$$

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

$$1$$