Find the Derivative - d/dx (x+x^-1)^3

Problem

d()/d(x)*(x+x(−1))3

Solution

1. Identify the outer function and the inner function to apply the Chain Rule, which states d(un)/d(x)=n*u(n−1)d(u)/d(x)

2. Apply the Power Rule to the outer function by bringing the exponent 3 to the front and decreasing the power by 1

3*(x+x(−1))2⋅d(x+x(−1))/d(x)

3. Differentiate the inner expression x+x(−1) term by term using the Power Rule.

d(x)/d(x)+d(x(−1))/d(x)=1−x(−2)

4. Combine the results of the outer and inner derivatives.

3*(x+x(−1))2*(1−x(−2))

5. Simplify the expression by rewriting the negative exponents as fractions if desired.

3*(x+1/x)2*(1−1/(x2))

Final Answer

d(x+x(−1))/d(x)=3*(x+x(−1))2*(1−x(−2))

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