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

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

Evaluate

$$8x^{12}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 4 and 8 to get 12.

$$4x^{12}\times 2$$

Multiply 4 and 2 to get 8.

$$8x^{12}$$

Differentiate w.r.t. x

$$96x^{11}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 4 and 8 to get 12.

$$\frac{\mathrm{d}}{\mathrm{d}x}(4x^{12}\times 2)$$

Multiply 4 and 2 to get 8.

$$\frac{\mathrm{d}}{\mathrm{d}x}(8x^{12})$$

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

$$12\times 8x^{12-1}$$

Multiply 12 times 8.

$$96x^{12-1}$$

Subtract 1 from 12.

$$96x^{11}$$