Solve a/a^frac{3{2}}

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

Evaluate

$$\frac{1}{\sqrt{a}}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{a^{1}}{a^{\frac{3}{2}}}$$

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

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

Subtract \frac{3}{2} from 1.

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

Differentiate w.r.t. a

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

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{1}{1}a^{1-\frac{3}{2}})$$

Do the arithmetic.

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

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}.

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

Do the arithmetic.

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