Solve (2x)(4x)

$$( 2 x ) ( 4 x )$$

Evaluate

$$8x^{2}$$

Solution Steps

Multiply x and x to get x^{2}.

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

Multiply 2 and 4 to get 8.

$$8x^{2}$$

Differentiate w.r.t. x

$$16x$$

Steps Using Definition of a Derivative

Multiply x and x to get x^{2}.

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

Multiply 2 and 4 to get 8.

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

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

$$2\times 8x^{2-1}$$

Multiply 2 times 8.

$$16x^{2-1}$$

Subtract 1 from 2.

$$16x^{1}$$

For any term t, t^{1}=t.

$$16x$$