Solve 6a^3*2a^3

$$6 a ^ { 3 } \cdot 2 a ^ { 3 }$$

Evaluate

$$12a^{6}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 3 to get 6.

$$6a^{6}\times 2$$

Multiply 6 and 2 to get 12.

$$12a^{6}$$

Differentiate w.r.t. a

$$72a^{5}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 3 and 3 to get 6.

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

Multiply 6 and 2 to get 12.

$$\frac{\mathrm{d}}{\mathrm{d}a}(12a^{6})$$

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

$$6\times 12a^{6-1}$$

Multiply 6 times 12.

$$72a^{6-1}$$

Subtract 1 from 6.

$$72a^{5}$$