Find the Derivative - d/dx h(x)=(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, where the outer function is u3 and the inner function is u=x+x(−1)

2. Apply the power rule to the outer function by bringing the exponent to the front and decreasing the exponent by one.

3*(x+x(−1))2⋅d()/d(x)*(x+x(−1))

3. Differentiate the inner expression x+x(−1) using the power rule for each term.

d(x)/d(x)+d(x(−1))/d(x)=1−x(−2)

4. Combine the results of the chain rule steps.

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

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