Find the Derivative - d/dx x/11-11/x

Problem

d()/d(x)*(x/11−11/x)

Solution

1. Rewrite the expression to make differentiation easier by expressing the terms as powers of x

x/11−11/x=1/11*x−11*x(−1)

2. Apply the sum rule for derivatives, which allows for the differentiation of each term independently.

d()/d(x)*(1/11*x−11*x(−1))=d()/d(x)1/11*x−d()/d(x)*11*x(−1)

3. Apply the power rule d(xn)/d(x)=n*x(n−1) to both terms.

d()/d(x)1/11*x=1/11

d()/d(x)*11*x(−1)=11*(−1)*x(−2)=−11*x(−2)

4. Combine the results and simplify the signs.

1/11−(−11*x(−2))=1/11+11*x(−2)

5. Rewrite the expression using positive exponents.

1/11+11/(x2)

Final Answer

d()/d(x)*(x/11−11/x)=1/11+11/(x2)

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