Solve (x)(x)(-x)

$$(x)(x)(-x)$$

Evaluate

$$-x^{3}$$

Solution Steps

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

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

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

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

Differentiate w.r.t. x

$$-3x^{2}$$

Steps Using Definition of a Derivative

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

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

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{3}\left(-1\right))$$

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

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

Multiply 3 times -1.

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

Subtract 1 from 3.

$$-3x^{2}$$