Find dy/dx 9x^2+y^2=9

Problem

9*x2+y2=9

Solution

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

(d(9)*x2)/d(x)+d(y2)/d(x)=d(9)/d(x)

2. Apply the power rule to 9*x2 and the chain rule to y2

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

3. Isolate the term containing d(y)/d(x) by subtracting 18*x from both sides.

2*yd(y)/d(x)=−18*x

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

d(y)/d(x)=(−18*x)/(2*y)

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

d(y)/d(x)=−(9*x)/y

Final Answer

d(y)/d(x)=−(9*x)/y

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