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If x=e^(sin^(-1)y) then (dy)/(dx)|(x=1)...

If `x=e^(sin^(-1)y)` then `(dy)/(dx)|_(x=1)`

A

`-1`

B

2

C

`1//2`

D

1

Text Solution

Verified by Experts

The correct Answer is:
D
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MCGROW HILL PUBLICATION-DIFFERENTIABILITY AND DIFFERENTIATION -Questions from Previous Years. B-Architecture Entrance Examination Papers
  1. If x=e^(sin^(-1)y) then (dy)/(dx)|(x=1)

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  2. Let f(x)={{:(ax" ,",,x lt 2),(ax^(2)+bx+3",",,x ge 2):} If f is...

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  3. Let f:[0,oo)to [0,oo) be given by f(x)=overset(10)underset(i=1)sum(x...

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  4. Let f:(-oo,oo)to(-oo,oo) be given by f(x)=x|x|+|x-1|-|x-2|^(2)+|x-3|...

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  5. Let f(.) and g(.) be differentiable functions on (-oo,oo) and let f'(....

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  6. Let f:(-oo,oo)to(-oo,oo) be defined by f(x)={{:(x^(2)",",,"if "x gt ...

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  7. Let f:R to R and g:R to R be functions defined by f(x)=sgn (sin x),g(x...

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  8. Let f(x)=2tan^(-1)((1+x)/(1-x))+sin^(-1)((1-x^(2))/(1+x^(2))),x in R, ...

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  9. If f(x)={{:(1-x^(2)",",,x le -1),(2x+2",",,x gt -1):} then the derivat...

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  10. Amongst the following functions, a function that is differentiable at ...

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  11. Let f be a differentiable function such that 8f(x)+6f((1)/(x))-x=5(x n...

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  12. If f(x)={{:((1)/(|x|),,"if "|x|gt2),(a+bx^(2),,"if "|x|le2):} then f...

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  13. Let y(x)=(1+x)(1+x^(2))(1+x^(4))…(1+x^(32)). Then (dy)/(dx) at x=(1)/(...

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  14. If y(x)=|{:(sin x,, cos x,, sinx+cosx+1),(23,,17,,13),(1,,1,,1):}|,x i...

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  15. If the function f:R to R defined by f(x)={{:(ax,,x lt 2),(ax^(2)-bx+...

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  16. If y=y(x) is an implicit function of x given by y cos x+x cos y=pi, th...

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  17. For f(x)={{:(x(e^(1//x)-e^(1//x))/(e^(1//x)+e^(-1//x))",",, x ne 0),(0...

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