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If x=e^(y+e^(y+e^(y+...oo))),xgt0, then...

If `x=e^(y+e^(y+e^(y+...oo))),xgt0`, then `(dy)/(dx)` is equal to

A

`(x)/(1+x)`

B

`(1+x)/(x)`

C

`(1-x)/(x)`

D

`(1)/(x)`

Text Solution

Verified by Experts

The correct Answer is:
C
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ARIHANT MATHS-DIFFERENTIATION -Exercise (More Than One Correct Option Type Questions)
  1. "If "xsqrt(1+y)+ysqrt(1+x)=0," prove that "(dy)/(dx)=-(1)/((x+1)^(2)).

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  2. If x^2e^y+2xye^x+13=0 then (dy)/(dx)=

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  3. If x=e^(y+e^(y+e^(y+...oo))),xgt0, then (dy)/(dx) is equal to

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  4. Let g be the inverse function of f and f'(x)=(x^(10))/(1+x^(2)). If g(...

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  5. If f and g are the function whose graphs are as shown, let u(x)=f(g(x)...

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  6. f'(x) = g(x) and g'(x) =-f(x) for all real x and f(5)=2=f'(5) then f^2...

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  7. if f(x) = x +x^2/1! + x^3/2! +----+ x^n/(n-1)! then f(0) + f'(0) + f'...

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  8. If y=(f(0)f(0)f)(x)andf(0)=0,f'(0)=2 then y'(0) is equal to

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  9. If y^2=P(x) is a polynomial of degree 3, then 2(d/(dx))(y^2dot(d^2y)/(...

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  10. If y=f(x)andx=g(y) are inverse functions of each other, then

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  11. If y is a function of x then (d^2y)/(dx^2)+y \ dy/dx=0. If x is a func...

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  12. Let g(x) = log f(x), where f(x) is a twice differentiable positive fun...

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  13. If the functions f(x)=x^(3)+e^(x//2) " and " g(x)=f^(-1)(x), the value...

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  14. Let f(theta)=sin(tan^(-1)((sintheta)/(sqrt(cos2theta)))), where -pi/4...

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  15. If y=log(sinx)(tanx), then (dy)/ (dx) at x=(pi)/(4) is equal to

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  16. If y=sum(r=1)^(x) tan^(-1)((1)/(1+r+r^(2))), then (dy)/(dx) is equal t...

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  17. If f(x)=cot^(-1)((x^(x)-x^(-x))/(2)) then f'(1) equals

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  18. The function f(x)=e^x+x , being differentiable and one-to-one, has a d...

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  19. If f''(x)=-f(x) and g(x)=f^(prime)(x) and F(x)=(f(x/2))^2+(g(x/2))^2 a...

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  20. Write the subsets of {1,2}.

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