Solve 2a^-3*a^frac{2{3}}

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

Differentiate w.r.t. a

$$-\frac{14}{3a^{\frac{10}{3}}}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add -3 and \frac{2}{3} to get -\frac{7}{3}.

$$\frac{\mathrm{d}}{\mathrm{d}a}(2a^{-\frac{7}{3}})$$

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

$$-\frac{7}{3}\times 2a^{-\frac{7}{3}-1}$$

Multiply -\frac{7}{3} times 2.

$$-\frac{14}{3}a^{-\frac{7}{3}-1}$$

Subtract 1 from -\frac{7}{3}.

$$-\frac{14}{3}a^{-\frac{10}{3}}$$

Evaluate

$$\frac{2}{a^{\frac{7}{3}}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -3 and \frac{2}{3} to get -\frac{7}{3}.

$$2a^{-\frac{7}{3}}$$