Solve 1/2x*-2x

$$\frac{ 1 }{ 2 } x \times -2x$$

Evaluate

$$-x^{2}$$

Solution Steps

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

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

Multiply \frac{1}{2} and -2 to get \frac{-2}{2}.

$$\frac{-2}{2}x^{2}$$

Divide -2 by 2 to get -1.

$$-x^{2}$$

Differentiate w.r.t. x

$$-2x$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{2}x^{2}\left(-2\right))$$

Multiply \frac{1}{2} and -2 to get \frac{-2}{2}.

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

Divide -2 by 2 to get -1.

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

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

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

Multiply 2 times -1.

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

Subtract 1 from 2.

$$-2x^{1}$$

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

$$-2x$$