Solve 3a^2*2a^3

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

Evaluate

$$6a^{5}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

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

Multiply 3 and 2 to get 6.

$$6a^{5}$$

Differentiate w.r.t. a

$$30a^{4}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$\frac{\mathrm{d}}{\mathrm{d}a}(3a^{5}\times 2)$$

Multiply 3 and 2 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}a}(6a^{5})$$

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

$$5\times 6a^{5-1}$$

Multiply 5 times 6.

$$30a^{5-1}$$

Subtract 1 from 5.

$$30a^{4}$$