Solve (3a^2)(6a^10)

$$( 3 a ^ { 2 } ) ( 6 a ^ { 10 } )$$

Evaluate

$$18a^{12}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 10 to get 12.

$$3a^{12}\times 6$$

Multiply 3 and 6 to get 18.

$$18a^{12}$$

Differentiate w.r.t. a

$$216a^{11}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 2 and 10 to get 12.

$$\frac{\mathrm{d}}{\mathrm{d}a}(3a^{12}\times 6)$$

Multiply 3 and 6 to get 18.

$$\frac{\mathrm{d}}{\mathrm{d}a}(18a^{12})$$

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

$$12\times 18a^{12-1}$$

Multiply 12 times 18.

$$216a^{12-1}$$

Subtract 1 from 12.

$$216a^{11}$$