Solve (-{left(sqrt{6+x}right)}^2

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

Evaluate

$$-\left(x+6\right)$$

Solution Steps

Calculate \sqrt{6+x} to the power of 2 and get 6+x.

$$-\left(6+x\right)$$

To find the opposite of 6+x, find the opposite of each term.

$$-6-x$$

Differentiate w.r.t. x

$$-1$$

Steps Using Derivative Rule for Sum

Calculate \sqrt{6+x} to the power of 2 and get 6+x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-\left(6+x\right))$$

To find the opposite of 6+x, find the opposite of each term.

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

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.

$$-1$$