Find dy/dx 1/x+1/y=1

Problem

1/x+1/y=1

Solution

1. Rewrite the equation using negative exponents to make differentiation easier.

1/x+1/y=1⇒x(−1)+y(−1)=1

2. Differentiate both sides of the equation with respect to x applying the chain rule to the term involving y

d(x(−1))/d(x)+d(y(−1))/d(x)=d(1)/d(x)

3. Apply the power rule and the chain rule.

−x(−2)−y(−2)d(y)/d(x)=0

4. Isolate the term containing d(y)/d(x) by adding x(−2) to both sides.

−y(−2)d(y)/d(x)=x(−2)

5. Solve for d(y)/d(x) by dividing both sides by −y(−2)

d(y)/d(x)=(x(−2))/(−y(−2))

6. Simplify the expression by moving the variables to the opposite parts of the fraction to eliminate negative exponents.

d(y)/d(x)=−(y2)/(x2)

Final Answer

d(y)/d(x)=−(y2)/(x2)

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