Solve 3a^3*3a^3

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

Evaluate

$$9a^{6}$$

Solution Steps

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

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

Multiply 3 and 3 to get 9.

$$9a^{6}$$

Differentiate w.r.t. a

$$54a^{5}$$

Steps Using Definition of a Derivative

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

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

Multiply 3 and 3 to get 9.

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

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

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

Multiply 6 times 9.

$$54a^{6-1}$$

Subtract 1 from 6.

$$54a^{5}$$