Solve -1/2x*12x

$$- \frac{ 1 }{ 2 } x \times 12x$$

Evaluate

$$-6x^{2}$$

Solution Steps

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

$$-\frac{1}{2}x^{2}\times 12$$

Express -\frac{1}{2}\times 12 as a single fraction.

$$\frac{-12}{2}x^{2}$$

Divide -12 by 2 to get -6.

$$-6x^{2}$$

Differentiate w.r.t. x

$$-12x$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(-\frac{1}{2}x^{2}\times 12)$$

Express -\frac{1}{2}\times 12 as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-12}{2}x^{2})$$

Divide -12 by 2 to get -6.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-6x^{2})$$

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

$$2\left(-6\right)x^{2-1}$$

Multiply 2 times -6.

$$-12x^{2-1}$$

Subtract 1 from 2.

$$-12x^{1}$$

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

$$-12x$$