Solve 4/3a^-3/2a^1/6

$$4 / 3 a ^ { - 3 / 2 } a ^ { 1 / 6 }$$

Differentiate w.r.t. a

$$-\frac{16}{9a^{\frac{7}{3}}}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add -\frac{3}{2} and \frac{1}{6} to get -\frac{4}{3}.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{4}{3}a^{-\frac{4}{3}})$$

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

$$-\frac{4}{3}\times \frac{4}{3}a^{-\frac{4}{3}-1}$$

Multiply -\frac{4}{3} times \frac{4}{3} by multiplying numerator times numerator and denominator times denominator. Then reduce the fraction to lowest terms if possible.

$$-\frac{16}{9}a^{-\frac{4}{3}-1}$$

Subtract 1 from -\frac{4}{3}.

$$-\frac{16}{9}a^{-\frac{7}{3}}$$

Evaluate

$$\frac{4}{3a^{\frac{4}{3}}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -\frac{3}{2} and \frac{1}{6} to get -\frac{4}{3}.

$$\frac{4}{3}a^{-\frac{4}{3}}$$