Find dy/dx (x+2)^2+(y-3)^2=37

Problem

(x+2)2+(y−3)2=37

Solution

1. Differentiate both sides of the equation with respect to x using the chain rule for terms involving y

d(x+2)/d(x)+d(y−3)/d(x)=d(37)/d(x)

2. Apply the power rule and chain rule to the terms on the left side.

2*(x+2)+2*(y−3)d(y)/d(x)=0

3. Isolate the term containing d(y)/d(x) by subtracting 2*(x+2) from both sides.

2*(y−3)d(y)/d(x)=−2*(x+2)

4. Solve for d(y)/d(x) by dividing both sides by 2*(y−3)

d(y)/d(x)=(−2*(x+2))/(2*(y−3))

5. Simplify the fraction by canceling the common factor of 2

d(y)/d(x)=−(x+2)/(y−3)

Final Answer

d(y)/d(x)=−(x+2)/(y−3)

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