Find dy/dx 9x^2-y^2=1

Problem

9*x2−y2=1

Solution

1. Differentiate both sides of the equation with respect to x treating y as a function of x

(d(9)*x2)/d(x)−d(y2)/d(x)=d(1)/d(x)

2. Apply the power rule to the first term and the chain rule to the second term.

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 resulting 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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