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

Problem

d()/d(x)1/(x2−1)

Solution

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

1/(x2−1)=(x2−1)(−1)

2. Apply the power rule and the chain rule by bringing the exponent to the front and subtracting one from the exponent.

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

3. Differentiate the inner function x2−1 with respect to x

d(x2−1)/d(x)=2*x

4. Substitute the derivative of the inner function back into the expression.

−1*(x2−1)(−2)⋅2*x=−2*x*(x2−1)(−2)

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

−2*x*(x2−1)(−2)=(−2*x)/((x2−1)2)

Final Answer

d()/d(x)1/(x2−1)=(−2*x)/((x2−1)2)

Want more problems? Check here!