Solve xdivx^frac{1{2}}

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

Evaluate

$$\sqrt{x}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{x^{1}}{\sqrt{x}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

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

Subtract \frac{1}{2} from 1.

$$\sqrt{x}$$

Differentiate w.r.t. x

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

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

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

Do the arithmetic.

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

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

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

Do the arithmetic.

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