Find dy/dx 2x^2+y^2=66

Problem

2*x2+y2=66

Solution

1. Differentiate both sides with respect to x treating y as a function of x and applying the chain rule to the y2 term.

d()/d(x)*(2*x2+y2)=d()/d(x)*66

2. Apply the power rule to 2*x2 and the chain rule to y2

4*x+2*yd(y)/d(x)=0

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

2*yd(y)/d(x)=−4*x

4. Solve for the derivative by dividing both sides by 2*y

d(y)/d(x)=(−4*x)/(2*y)

5. Simplify the fraction by dividing the numerator and denominator by 2.

d(y)/d(x)=−(2*x)/y

Final Answer

d(y)/d(x)=−(2*x)/y

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