Solve a^-frac{3{5}}*a^frac{5{2}}*a^2*a^0

$$a ^ { - \frac { 3 } { 5 } } \cdot a ^ { \frac { 5 } { 2 } } \cdot a ^ { 2 } \cdot a ^ { 0 }$$

Differentiate w.r.t. a

$$\frac{39a^{\frac{29}{10}}}{10}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add -\frac{3}{5} and \frac{5}{2} to get \frac{19}{10}.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{\frac{19}{10}}a^{2}a^{0})$$

To multiply powers of the same base, add their exponents. Add \frac{19}{10} and 2 to get \frac{39}{10}.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{\frac{39}{10}}a^{0})$$

To multiply powers of the same base, add their exponents. Add \frac{39}{10} and 0 to get \frac{39}{10}.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{\frac{39}{10}})$$

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

$$\frac{39}{10}a^{\frac{39}{10}-1}$$

Subtract 1 from \frac{39}{10}.

$$\frac{39}{10}a^{\frac{29}{10}}$$

Evaluate

$$a^{\frac{39}{10}}$$