AIEEE 2004
JEE Main 2004 Mathematics question on Limits Continuity and Differentiability
If
y is a function of
x and
log(x+y)=2xy, then the value of
y′(0) is
- A.
1
- B.
- C.
2
- D.
0
Show answer and solution
Correct option: A
Solution
Differentiate log(x + y) = 2xy implicitly:
(1 + y')/(x + y) = 2y + 2xy'
At x = 0: first find y(0) by substituting x = 0 into the original equation → log(0 + y) = 0, so log y = 0, giving y(0) = 1.
Now substitute x = 0, y = 1:
(1 + y')/1 = 2(1) + 0 → 1 + y' = 2 → y'(0) = 1.
[AIEEE 2004]
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