Solve 4x^2*8x

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

Evaluate

$$32x^{3}$$

Solution Steps

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

$$4x^{3}\times 8$$

Multiply 4 and 8 to get 32.

$$32x^{3}$$

Differentiate w.r.t. x

$$96x^{2}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(4x^{3}\times 8)$$

Multiply 4 and 8 to get 32.

$$\frac{\mathrm{d}}{\mathrm{d}x}(32x^{3})$$

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

$$3\times 32x^{3-1}$$

Multiply 3 times 32.

$$96x^{3-1}$$

Subtract 1 from 3.

$$96x^{2}$$