Find the Derivative - d/dx x+16/x

Problem

d()/d(x)*(x+16/x)

Solution

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

16/x=16*x(−1)

2. Apply the sum rule to differentiate each term of the expression separately.

d()/d(x)*(x+16*x(−1))=d(x)/d(x)+(d(16)*x(−1))/d(x)

3. Apply the power rule which states that d(xn)/d(x)=n*x(n−1) for both terms.

d(x)/d(x)=1

(d(16)*x(−1))/d(x)=16*(−1)*x(−2)

4. Simplify the resulting expression by combining the terms and converting the negative exponent back into a fraction.

−16*x(−2)=−16/(x2)

Final Answer

d()/d(x)*(x+16/x)=1−16/(x2)

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