If 3x + 3y = 3x + y, then find dy dx .
We can see that complete solution: write formula, plug data, do arithmetic. Final value matches 3^x+y - 3^x3^y - 3^x+y. Simple and accurate.
Ref: NCERT Mathematics Class XII — Differential Equations
#implicit differentiation
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If y = 4x - 5 is tangent to the curve y² = px³ + q at (2, 3), then
The logic is straightforward: after simplifying, p = 2, q = -7 is left. The method is simple: formula → substitution → calculation → answer.
Ref: NCERT Mathematics Class XII — Applications of Derivatives
The points on the curve y³ + 3x² = 12y where the tangent is vertical, is (are)
Think of it like this: complete solution: write formula, plug data, do arithmetic. Final value matches ( 4/ 3 , 2 ). Simple and accurate.
Ref: NCERT Mathematics Class XII — Applications of Derivatives
