Solve =x^2/x^frac{1{2}}

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

Evaluate

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

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

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

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

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

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

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

Differentiate w.r.t. x

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

Solution Steps

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

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

Do the arithmetic.

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

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}.

$$\frac{3}{2}x^{\frac{3}{2}-1}$$

Do the arithmetic.

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