Find the Derivative - d/dy 1/y

Problem

d()/d(y)1/y

Solution

1. Rewrite the expression using a negative exponent to make it easier to differentiate.

1/y=y(−1)

2. Apply the power rule for derivatives, which states that d(yn)/d(y)=n*y(n−1)

d(y(−1))/d(y)=−1⋅y(−1−1)

3. Simplify the exponent.

−1⋅y(−2)=−y(−2)

4. Rewrite the result back into fractional form by moving the variable to the denominator.

−y(−2)=−1/(y2)

Final Answer

d()/d(y)1/y=−1/(y2)

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