Question
Passage: Let (e^y )^x-y=0, where y is a function of x whose domain is (0,10]. Question: What is dy dx equal to ?
NDA
Mathematics
Differentiation
2026
NDA 2026 (Phase 1)
NDA Mathematics Question (2026) — Solution
Options
- A. y 1-xy
- B. y 1+xy
- C. y^2 1-xy
- D. y^2 1+xy
Answer
C. y^2 1-xy
Step-by-step solution
Given equation is (e^y)^x - y = 0 e^ xy = y Taking natural logarithm on both sides: xy = (y) Differentiating both sides with respect to x: y + x dy dx = 1 y dy dx y = ( 1 y - x ) dy dx y = ( 1 - xy y ) dy dx dy dx = y^2 1 - xy
Related: Mathematics — Differentiation · All PYQ Banks