Find the Derivative - d/dx y=x/3-3/x

Problem

d()/d(x)*(x/3−3/x)

Solution

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

x/3−3/x=1/3*x−3*x(−1)

2. Apply the power rule which states that d(xn)/d(x)=n*x(n−1) to each term independently.

d()/d(x)1/3*x=1/3

d()/d(x)*(−3*x(−1))=(−3)*(−1)*x(−2)=3*x(−2)

3. Combine the results of the derivatives.

1/3+3*x(−2)

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

1/3+3/(x2)

Final Answer

d()/d(x)*(x/3−3/x)=1/3+3/(x2)

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