Find the Derivative - d/dx 1/(x^2-4)

Problem

d()/d(x)1/(x2−4)

Solution

1. Rewrite the expression using a negative exponent to prepare for the power rule and chain rule.

1/(x2−4)=(x2−4)(−1)

2. Apply the power rule by bringing the exponent down and subtracting one from the exponent.

d(x2−4)/d(x)=−1*(x2−4)(−2)⋅d(x2−4)/d(x)

3. Apply the chain rule by multiplying by the derivative of the inner function x2−4

d(x2−4)/d(x)=2*x

4. Combine the results of the differentiation.

−1*(x2−4)(−2)⋅2*x=−2*x*(x2−4)(−2)

5. Simplify the expression by moving the term with the negative exponent back to the denominator.

−2*x*(x2−4)(−2)=(−2*x)/((x2−4)2)

Final Answer

d()/d(x)1/(x2−4)=(−2*x)/((x2−4)2)

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