Find the Derivative - d/dx x/10-10/x

Problem

d()/d(x)*(x/10−10/x)

Solution

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

x/10−10/x=1/10*x−10*x(−1)

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

d()/d(x)*(1/10*x−10*x(−1))=d()/d(x)1/10*x−d()/d(x)*10*x(−1)

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

d()/d(x)1/10*x=1/10

d()/d(x)*10*x(−1)=−10*x(−2)

4. Combine the results and simplify the signs.

1/10−(−10*x(−2))=1/10+10*x(−2)

5. Rewrite the expression back into fraction form.

1/10+10/(x2)

Final Answer

d()/d(x)*(x/10−10/x)=1/10+10/(x2)

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