Find dy/dx y=-x/y

Problem

y=−x/y

Solution

1. Rewrite the equation to eliminate the fraction by multiplying both sides by y

y2=−x

2. Differentiate both sides of the equation with respect to x using implicit differentiation.

d(y2)/d(x)=(d(−)*x)/d(x)

3. Apply the chain rule to the left side and the power rule to the right side.

2*yd(y)/d(x)=−1

4. Solve for d(y)/d(x) by dividing both sides by 2*y

d(y)/d(x)=−1/(2*y)

Final Answer

d(y)/d(x)=−1/(2*y)

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