Find dy/dx xy=6

Problem

x*y=6

Solution

1. Differentiate both sides of the equation with respect to x

(d(x)*y)/d(x)=d(6)/d(x)

2. Apply the product rule to the left side, where (d(u)*v)/d(x)=ud(v)/d(x)+vd(u)/d(x)

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

3. Simplify the expression by noting that d(x)/d(x)=1

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

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

xd(y)/d(x)=−y

5. Solve for d(y)/d(x) by dividing both sides by x

d(y)/d(x)=−y/x

Final Answer

d(y)/d(x)=−y/x

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