Solve x^2/x^9/2

$$\frac { x ^ { 2 } } { x ^ { 9 / 2 } }$$

Evaluate

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

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{x^{2}}{x^{\frac{9}{2}}}$$

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

$$x^{2-\frac{9}{2}}$$

Subtract \frac{9}{2} from 2.

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

Differentiate w.r.t. x

$$-\frac{5}{2x^{\frac{7}{2}}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{1}x^{2-\frac{9}{2}})$$

Do the arithmetic.

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

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}.

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

Do the arithmetic.

$$-\frac{5}{2}x^{-\frac{7}{2}}$$