Solve -2(sqrt{x+4})^2-5

$$- 2 ( \sqrt { x + 4 } ) ^ { 2 } - 5$$

Evaluate

$$-2x-13$$

Solution Steps

Calculate \sqrt{x+4} to the power of 2 and get x+4.

$$-2\left(x+4\right)-5$$

Use the distributive property to multiply -2 by x+4.

$$-2x-8-5$$

Subtract 5 from -8 to get -13.

$$-2x-13$$

Differentiate w.r.t. x

$$-2$$

Steps Using Derivative Rule for Sum

Calculate \sqrt{x+4} to the power of 2 and get x+4.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-2\left(x+4\right)-5)$$

Use the distributive property to multiply -2 by x+4.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-2x-8-5)$$

Subtract 5 from -8 to get -13.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-2x-13)$$

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}.

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

Subtract 1 from 1.

$$-2x^{0}$$

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

$$-2$$