Find the Derivative - d/dx x/7-7/x

Problem

d()/d(x)*(x/7−7/x)

Solution

1. Rewrite the expression using power notation to make differentiation easier.

x/7−7/x=1/7*x−7*x(−1)

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

d()/d(x)*(1/7*x−7*x(−1))=(d(1/7)*x)/d(x)−(d(7)*x(−1))/d(x)

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

(d(1/7)*x)/d(x)=1/7

(d(7)*x(−1))/d(x)=7*(−1)*x(−2)=−7*x(−2)

4. Combine the results and simplify the signs.

1/7−(−7*x(−2))=1/7+7*x(−2)

5. Rewrite the final expression using positive exponents.

1/7+7/(x2)

Final Answer

d()/d(x)*(x/7−7/x)=1/7+7/(x2)

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