Solve (3a^2)(5a^6)

$$( 3 a ^ { 2 } ) ( 5 a ^ { 6 } )$$

Evaluate

$$15a^{8}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 6 to get 8.

$$3a^{8}\times 5$$

Multiply 3 and 5 to get 15.

$$15a^{8}$$

Differentiate w.r.t. a

$$120a^{7}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 2 and 6 to get 8.

$$\frac{\mathrm{d}}{\mathrm{d}a}(3a^{8}\times 5)$$

Multiply 3 and 5 to get 15.

$$\frac{\mathrm{d}}{\mathrm{d}a}(15a^{8})$$

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

$$8\times 15a^{8-1}$$

Multiply 8 times 15.

$$120a^{8-1}$$

Subtract 1 from 8.

$$120a^{7}$$