Solve sqrt{x}div3sqrt{x}

$$\sqrt { x } \div 3 \sqrt { x }$$

Evaluate

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

Solution Steps

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

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

Multiply \sqrt{x} and \sqrt{x} to get \left(\sqrt{x}\right)^{2}.

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

Calculate \sqrt{x} to the power of 2 and get x.

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

Differentiate w.r.t. x

$$\frac{1}{3} = 0.3333333333333333$$

Steps Using Definition of a Derivative

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

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

Multiply \sqrt{x} and \sqrt{x} to get \left(\sqrt{x}\right)^{2}.

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

Calculate \sqrt{x} to the power of 2 and get x.

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

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

$$\frac{1}{3}x^{1-1}$$

Subtract 1 from 1.

$$\frac{1}{3}x^{0}$$

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

$$\frac{1}{3}\times 1$$

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

$$\frac{1}{3}$$