FunctionHard
Question
Let y be an implicit function of x defined by x2x - 2xx cot y - 1 = 0. Then y′(1) equals
Options
A.-1
B.1
C.log 2
D.- log 2
Solution
x2x - 2xx cot y - 1 = 0 .....(1)
Now x = 1,
1 - 2 coty - 1 = 0 ⇒ coty = 0 ⇒ y =
Now differentiating eq. (1) w.r.t. ′x′
2x2x (1 + log x)- 2[xx(-cosec2y)
+ coty xx(1 + log x)] = 0
Now at
2(1 + log 1) - 2
= 0
⇒
Now x = 1,
1 - 2 coty - 1 = 0 ⇒ coty = 0 ⇒ y =
Now differentiating eq. (1) w.r.t. ′x′
2x2x (1 + log x)- 2[xx(-cosec2y)
+ coty xx(1 + log x)] = 0Now at
2(1 + log 1) - 2
= 0⇒
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