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Question
If `y=sqrt(sinx+sqrt(sinx+sqrt(sinx+....oo))),` then `dy/dx` equals ______.
Options
`cosx/(2y-1)`
`sinx/(1-2y)`
`sinx/(1+2y)`
`cosx/(1-2y)`
MCQ
Fill in the Blanks
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Solution
If `y=sqrt(sinx+sqrt(sinx+sqrt(sinx+....oo))),` then `dy/dx` equals `underline(cosx/(2y-1))`.
Explanation:
If `y=sqrt(f(x)+sqrt(f(x)+sqrt(f(x)+....oo))),` then
`dy/dx=(f^'(x))/(2y-1)`
`thereforedy/dx=cosx/(2y-1)`
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Derivative of Implicit Functions
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