Find dy/dx xy=1

Problem

x*y=1

Solution

1. Differentiate both sides with respect to x using the product rule on the left side and the constant rule on the right side.

2. Apply the product rule to the term x*y which states that (d(u)*v)/d(x)=ud(v)/d(x)+vd(u)/d(x)

xd(y)/d(x)+yd(x)/d(x)=d(1)/d(x)

3. Simplify the derivatives noting that d(x)/d(x)=1 and the derivative of a constant is 0

xd(y)/d(x)+y(1)=0

4. Isolate the term containing d(y)/d(x) by subtracting y from both sides.

xd(y)/d(x)=−y

5. Solve for the derivative by dividing both sides by x

d(y)/d(x)=−y/x

Final Answer

d(y)/d(x)=−y/x

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