Solve -(sqrt{-x-3})^2-3

$$- ( \sqrt { - x - 3 } ) ^ { 2 } - 3$$

Evaluate

$$x$$

Solution Steps

Calculate \sqrt{-x-3} to the power of 2 and get -x-3.

$$-\left(-x-3\right)-3$$

To find the opposite of -x-3, find the opposite of each term.

$$-\left(-x\right)+3-3$$

Subtract 3 from 3 to get 0.

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

Multiply -1 and -1 to get 1.

$$x$$

Differentiate w.r.t. x

$$1$$

Steps Using Definition of a Derivative

Calculate \sqrt{-x-3} to the power of 2 and get -x-3.

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

To find the opposite of -x-3, find the opposite of each term.

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

Subtract 3 from 3 to get 0.

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

Multiply -1 and -1 to get 1.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x)$$

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.

$$1$$