NDA 2025 · PYQ · Implicit differentiation · medium
Let (x + y)^(p+q) = x^p y^q, where p, q are positive integers. The derivative of y with respect to x
A.depends on p only
B.depends on q only
C.depends on both p and q
D.is independent of both p and q✓ Correct
Explanation
Taking logarithm: (p+q) ln(x+y) = p ln x + q ln y. Differentiating both sides w.r.t. x: (p+q)(1 + dy/dx)/(x+y) = p/x + (q/y)(dy/dx). Rearranging gives dy/dx = y/x after simplification. This result is independent of both p and q.
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