Solve 2a^frac{1{2}}*3a^frac{5{2}}

$$2 a ^ { \frac { 1 } { 2 } } \times 3 a ^ { \frac { 5 } { 2 } }$$

Evaluate

$$6a^{3}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add \frac{1}{2} and \frac{5}{2} to get 3.

$$2a^{3}\times 3$$

Multiply 2 and 3 to get 6.

$$6a^{3}$$

Differentiate w.r.t. a

$$18a^{2}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add \frac{1}{2} and \frac{5}{2} to get 3.

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

Multiply 2 and 3 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}a}(6a^{3})$$

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

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

Multiply 3 times 6.

$$18a^{3-1}$$

Subtract 1 from 3.

$$18a^{2}$$