Find the Derivative - d/dx x+9/x

Problem

d()/d(x)*(x+9/x)

Solution

1. Rewrite the expression using a negative exponent for the second term to make differentiation easier.

d()/d(x)*(x+9*x(−1))

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

d(x)/d(x)+(d(9)*x(−1))/d(x)

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

1+9*(−1)*x(−2)

4. Simplify the expression by multiplying the constants and converting the negative exponent back into a fraction.

1−9/(x2)

Final Answer

d()/d(x)*(x+9/x)=1−9/(x2)

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