`y^2 = (x^2 - 49)/(x^2 + 49), (7,0)` Find `dy/dx` by implicit differentiation and evaluate the derivative at the given point.

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gsarora17 eNotes educator| Certified Educator


Differentiating both sides with respect to x,






Now derivative at the point (7,0) can be evaluated by plugging in the value of x,y in dy/dx.

Since y=0 and it is in the denominator of dy/dx , so the derivative at the point(7,0) does not exist.