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

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

Evaluate

$$6a^{\frac{9}{2}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and \frac{5}{2} to get \frac{9}{2}.

$$2a^{\frac{9}{2}}\times 3$$

Multiply 2 and 3 to get 6.

$$6a^{\frac{9}{2}}$$

Differentiate w.r.t. a

$$27a^{\frac{7}{2}}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 2 and \frac{5}{2} to get \frac{9}{2}.

$$\frac{\mathrm{d}}{\mathrm{d}a}(2a^{\frac{9}{2}}\times 3)$$

Multiply 2 and 3 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}a}(6a^{\frac{9}{2}})$$

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

$$\frac{9}{2}\times 6a^{\frac{9}{2}-1}$$

Multiply \frac{9}{2} times 6.

$$27a^{\frac{9}{2}-1}$$

Subtract 1 from \frac{9}{2}.

$$27a^{\frac{7}{2}}$$