Solve (16x^2)(8x)

$$(16 { x }^{ 2 } )(8x)$$

Evaluate

$$128x^{3}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$16x^{3}\times 8$$

Multiply 16 and 8 to get 128.

$$128x^{3}$$

Differentiate w.r.t. x

$$384x^{2}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$\frac{\mathrm{d}}{\mathrm{d}x}(16x^{3}\times 8)$$

Multiply 16 and 8 to get 128.

$$\frac{\mathrm{d}}{\mathrm{d}x}(128x^{3})$$

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

$$3\times 128x^{3-1}$$

Multiply 3 times 128.

$$384x^{3-1}$$

Subtract 1 from 3.

$$384x^{2}$$