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

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

Evaluate

$$x^{2}-3$$

Solution Steps

Apply the distributive property by multiplying each term of -\sqrt{3}-x by each term of \sqrt{3}-x.

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

Multiply -1 and -1 to get 1.

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

Combine \sqrt{3}x and -x\sqrt{3} to get 0.

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

Differentiate w.r.t. x

$$2x$$

Steps Using Derivative Rule for Sum

Apply the distributive property by multiplying each term of -\sqrt{3}-x by each term of \sqrt{3}-x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(-\sqrt{3}\right)\sqrt{3}-\left(-\sqrt{3}\right)x-x\sqrt{3}+x^{2})$$

Multiply -1 and -1 to get 1.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(-\sqrt{3}\right)\sqrt{3}+\sqrt{3}x-x\sqrt{3}+x^{2})$$

Combine \sqrt{3}x and -x\sqrt{3} to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(-\sqrt{3}\right)\sqrt{3}+x^{2})$$

Multiply \sqrt{3} and \sqrt{3} to get 3.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-3+x^{2})$$

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}.

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

Subtract 1 from 2.

$$2x^{1}$$

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

$$2x$$