Solve (2x^4)(8x^15)

$$( 2 x ^ { 4 } ) ( 8 x ^ { 15 } )$$

Evaluate

$$16x^{19}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 4 and 15 to get 19.

$$2x^{19}\times 8$$

Multiply 2 and 8 to get 16.

$$16x^{19}$$

Differentiate w.r.t. x

$$304x^{18}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 4 and 15 to get 19.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{19}\times 8)$$

Multiply 2 and 8 to get 16.

$$\frac{\mathrm{d}}{\mathrm{d}x}(16x^{19})$$

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

$$19\times 16x^{19-1}$$

Multiply 19 times 16.

$$304x^{19-1}$$

Subtract 1 from 19.

$$304x^{18}$$