Solve 2*x^2*4x

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

Evaluate

$$8x^{3}$$

Solution Steps

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

$$2x^{3}\times 4$$

Multiply 2 and 4 to get 8.

$$8x^{3}$$

Differentiate w.r.t. x

$$24x^{2}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{3}\times 4)$$

Multiply 2 and 4 to get 8.

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

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

$$3\times 8x^{3-1}$$

Multiply 3 times 8.

$$24x^{3-1}$$

Subtract 1 from 3.

$$24x^{2}$$