Find dy/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=1/3*x

3/x=3*x(−1)

2. Apply the power rule to each term separately, where d(xn)/d(x)=n*x(n−1)

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

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

3. Combine the results using the sum and difference rule.

d(y)/d(x)=1/3−(−3*x(−2))

d(y)/d(x)=1/3+3*x(−2)

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

d(y)/d(x)=1/3+3/(x2)

Final Answer

d(y)/d(x)=1/3+3/(x2)

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