Solve frac{{a}^frac{1{3}}{a}^frac{5{6}}}{{a}^-frac{1{2}}}=

$$\frac{ { a }^{ \frac{ 1 }{ 3 } } { a }^{ \frac{ 5 }{ 6 } } }{ { a }^{ - \frac{ 1 }{ 2 } } } =$$

Differentiate w.r.t. a

$$\frac{5a^{\frac{2}{3}}}{3}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add \frac{1}{3} and \frac{5}{6} to get \frac{7}{6}.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{a^{\frac{7}{6}}}{a^{-\frac{1}{2}}})$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract -\frac{1}{2} from \frac{7}{6} to get \frac{5}{3}.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{\frac{5}{3}})$$

The derivative of ax^{n} is nax^{n-1}.

$$\frac{5}{3}a^{\frac{5}{3}-1}$$

Subtract 1 from \frac{5}{3}.

$$\frac{5}{3}a^{\frac{2}{3}}$$

Evaluate

$$a^{\frac{5}{3}}$$