Solve x^5/2/x^1/2=

$$\frac { x ^ { 5 / 2 } } { x ^ { 1 / 2 } } =$$

Evaluate

$$x^{2}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{x^{\frac{5}{2}}}{\sqrt{x}}$$

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

$$x^{\frac{5}{2}-\frac{1}{2}}$$

Subtract \frac{1}{2} from \frac{5}{2} by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$x^{2}$$

Differentiate w.r.t. x

$$2x$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{1}x^{\frac{5}{2}-\frac{1}{2}})$$

Do the arithmetic.

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

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}.

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

Do the arithmetic.

$$2x^{1}$$

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

$$2x$$