Solve (2a^3)(5a^4)

$$( 2 a ^ { 3 } ) ( 5 a ^ { 4 } )$$

Evaluate

$$10a^{7}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$2a^{7}\times 5$$

Multiply 2 and 5 to get 10.

$$10a^{7}$$

Differentiate w.r.t. a

$$70a^{6}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$\frac{\mathrm{d}}{\mathrm{d}a}(2a^{7}\times 5)$$

Multiply 2 and 5 to get 10.

$$\frac{\mathrm{d}}{\mathrm{d}a}(10a^{7})$$

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

$$7\times 10a^{7-1}$$

Multiply 7 times 10.

$$70a^{7-1}$$

Subtract 1 from 7.

$$70a^{6}$$