Implicit differentiation and related rates
\[xy^{2}-3x^2+y=25\]
\[P=(3,4)\]
Differentiate implicitly. At P, write the collected equation U+V y′=0, then give M=y′
For U and V, differentiate the displayed equation term by term exactly as written. Collect terms without multiplying or dividing the equation by a nonzero constant; then, when requested, substitute P. Keep all numerical factors introduced by differentiation