Find the Derivative - d/dx x+2/x

Problem

d()/d(x)*(x+2/x)

Solution

1. Apply the sum rule for differentiation, which allows for the derivative of each term to be taken separately.

d()/d(x)*(x+2/x)=d(x)/d(x)+d()/d(x)2/x

2. Rewrite the second term using a negative exponent to prepare for the power rule.

d()/d(x)2/x=d()/d(x)*2*x(−1)

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

d(x)/d(x)=1

(d(2)*x(−1))/d(x)=−2*x(−2)

4. Combine the results and simplify the expression by moving the negative exponent back to the denominator.

1−2*x(−2)=1−2/(x2)

Final Answer

d()/d(x)*(x+2/x)=1−2/(x2)

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