Solve (4x)(-2x)

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

Evaluate

$$-8x^{2}$$

Solution Steps

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

$$4x^{2}\left(-2\right)$$

Multiply 4 and -2 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}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(4x^{2}\left(-2\right))$$

Multiply 4 and -2 to get -8.

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

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

$$2\left(-8\right)x^{2-1}$$

Multiply 2 times -8.

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

Subtract 1 from 2.

$$-16x^{1}$$

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

$$-16x$$