Solve a^2/3*2a^-1/2

$$a ^ { 2 / 3 } \times 2 a ^ { - 1 / 2 }$$

Differentiate w.r.t. a

$$\frac{1}{3a^{\frac{5}{6}}}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add \frac{2}{3} and -\frac{1}{2} to get \frac{1}{6}.

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

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

$$\frac{1}{6}\times 2a^{\frac{1}{6}-1}$$

Multiply \frac{1}{6} times 2.

$$\frac{1}{3}a^{\frac{1}{6}-1}$$

Subtract 1 from \frac{1}{6}.

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

Evaluate

$$2\sqrt[6]{a}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add \frac{2}{3} and -\frac{1}{2} to get \frac{1}{6}.

$$a^{\frac{1}{6}}\times 2$$