Evaluate
\frac{2}{x+\sqrt{3}}
Differentiate w.r.t. x
-\frac{2}{\left(x+\sqrt{3}\right)^{2}}
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\frac{2\left(x-\sqrt{3}\right)}{\left(x+\sqrt{3}\right)\left(x-\sqrt{3}\right)}
Rationalize the denominator of \frac{2}{x+\sqrt{3}} by multiplying numerator and denominator by x-\sqrt{3}.
\frac{2\left(x-\sqrt{3}\right)}{x^{2}-\left(\sqrt{3}\right)^{2}}
Consider \left(x+\sqrt{3}\right)\left(x-\sqrt{3}\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.
\frac{2\left(x-\sqrt{3}\right)}{x^{2}-3}
The square of \sqrt{3} is 3.
\frac{2x-2\sqrt{3}}{x^{2}-3}
Use the distributive property to multiply 2 by x-\sqrt{3}.
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