Solve x*2x*(-2x)=

$$x \times 2 x \times ( - 2 x ) =$$

Evaluate

$$-4x^{3}$$

Solution Steps

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

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

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

$$x^{3}\times 2\left(-2\right)$$

Multiply 2 and -2 to get -4.

$$x^{3}\left(-4\right)$$

Differentiate w.r.t. x

$$-12x^{2}$$

Steps Using Definition of a Derivative

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

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

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{3}\times 2\left(-2\right))$$

Multiply 2 and -2 to get -4.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{3}\left(-4\right))$$

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

$$3\left(-4\right)x^{3-1}$$

Multiply 3 times -4.

$$-12x^{3-1}$$

Subtract 1 from 3.

$$-12x^{2}$$