Solve -sqrt{(}x-12)^2

$$- \sqrt { ( } x - 12 ) ^ { 2 }$$

Evaluate

$$12-x$$

Solution Steps

Calculate \sqrt{x-12} to the power of 2 and get x-12.

$$-\left(x-12\right)$$

To find the opposite of x-12, find the opposite of each term.

$$-x+12$$

Differentiate w.r.t. x

$$-1$$

Steps Using Derivative Rule for Sum

Calculate \sqrt{x-12} to the power of 2 and get x-12.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-\left(x-12\right))$$

To find the opposite of x-12, find the opposite of each term.

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

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

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

Subtract 1 from 1.

$$-x^{0}$$

For any term t except 0, t^{0}=1.

$$-1$$