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Let y be an implicit function of x defined by x² - 2x² cot y - 1 = 0. Then y'(1) equals
- 1
- log 2
- -log 2
- -1
Correct answer: -1
Solution
At x=1 the relation x^2-2x^2 cot y-1=0 gives -2 cot y=0, so cot y=0 and y=pi/2. Differentiating: 2x-4x cot y+2x^2 csc^2(y) y'=0. At x=1, cot y=0, csc^2 y=1: 2+2y'=0, so y'(1)=-1.
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