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

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

Evaluate

$$8x^{8}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 5 to get 8.

$$4x^{8}\times 2$$

Multiply 4 and 2 to get 8.

$$8x^{8}$$

Differentiate w.r.t. x

$$64x^{7}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 3 and 5 to get 8.

$$\frac{\mathrm{d}}{\mathrm{d}x}(4x^{8}\times 2)$$

Multiply 4 and 2 to get 8.

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

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

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

Multiply 8 times 8.

$$64x^{8-1}$$

Subtract 1 from 8.

$$64x^{7}$$