NDA 2026 · PYQ · Implicit Differentiation · medium
Let (e^y)^x - y = 0, where y is a function of x whose domain is (0, 10]. What is dy/dx equal to?
A.y/(1-xy)
B.y/(1+xy)
C.y²/(1-xy)✓ Correct
D.y²/(1+xy)
Explanation
From (e^y)^x = y, take ln: xy = ln y. Differentiate: y + x(dy/dx) = (1/y)(dy/dx). Rearranging: y = (dy/dx)(1/y - x) = (dy/dx)(1-xy)/y. So dy/dx = y²/(1-xy).
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