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"If "x=e^(y+e^(y^(+..."to"oo.)))," where...

`"If "x=e^(y+e^(y^(+..."to"oo.)))," where "xgt0," then find "(dy)/(dx).`

A

`(1+x)/(x)`

B

`(1)/(x)`

C

`(1-x)/(x)`

D

`(x)/(1+x)`

Text Solution

Verified by Experts

The correct Answer is:
C
We have,
`x=e^(y+e^(y+e^(y+..." to "oo)))`
`implies" "x=e^(y+x)`
`implies" "log_(e)x=(y+x)`
`implies" "(1)/(x)=(dy)/(dx)+1" "["Differentiating with respect to x"]`
`implies" "(dy)/(dx)=(1-x)/(x)`
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OBJECTIVE RD SHARMA ENGLISH-DIFFERENTIATION-Chapter Test
  1. "If "x=e^(y+e^(y^(+..."to"oo.)))," where "xgt0," then find "(dy)/(dx).

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  2. If f(x)=log(e)[log(e)x], then what is f' (e) equal to?

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  3. If e^y+xy=e then the value of (d^2y)/(dx^2) for x=0 is

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  4. If sqrt(x+y) +sqrt(y-x)=5, then (d^(2)y)/(dx ^(2))=

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  5. "If "ax^(2)+2hxy+by^(2)=1," then "(d^(2)y)/(dx^(2)) is

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  6. If f(x)=sin{(pi)/(2)[x]-x^(5)},1ltxlt2 and [.] denotes the greatest in...

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  7. f(x) is a polynomial of degree

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  8. If y=sin(log(e)x), then x^(2)(d^(2)y)/(dx^(2))+x(dy)/(dx) is equal to

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  9. If f(x)=(1-x)^n, then the value of f(0)+f^(prime)(0)+(f^('')(0))/(2!)+...

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  10. "If "xsqrt(1+y)+ysqrt(1+x)=0," prove that "(dy)/(dx)=-(1)/((x+1)^(2)).

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  11. If 8f(x)+6f(1/x)=x+5 and y=x^2(f(x), then (dy)/(dx) at x=-1 is equal t...

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  12. If y=sin^(-1){(5x+12 sqrt(1-x^(2)))/(13)}, find (dy)/(dx).

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  13. If f(x)=cos^(-1){(1-(log(e)x)^(2))/(1+(log(e)x)^(2))}, then f'( e )

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  14. y=sin^(-1)[sqrt(x-ax)-sqrt(a-ax)]

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  15. Let f(x)=(x^3+2)^(30) If f^n (x) is a polynomial of degree 20 where f^...

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  16. If f(x)=cos^(2)x+cos^(2)(x+(pi)/(3))+sinxsin(x+(pi)/(3)) and g((5)/(4)...

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  17. If f(x)=10cosx+(13+2x)sinx then f''(x)+f(x)=

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  18. Let a function f:RtoR satisfy the equation f(x+y)=f(x)=f(Y)AAx, yepsil...

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  19. If f(x)=log{(u(x))/(v(x))},\ u(1)=v(1) and u^(prime)(1)=v^(prime)(1)=2...

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  20. If f'(x)=arc tan((x^(x)-x^(-x))/(2)), then f'(1) is equal to

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  21. Let f(x)=2^(2x-1)" and "g(x)=-2^(x)+2xlog2. Then the set of points sat...

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