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If y=e^(sqrt(x))+e^(-sqrt(x)) , then (dy...

If `y=e^(sqrt(x))+e^(-sqrt(x))` , then `(dy)/(dx)i se q u a lto` `(e^(sqrt(x)))/(2sqrt(x))` (b) `(e^(sqrt(x))-e^(-sqrt(x)))/(2x)` `1/(2sqrt(x))sqrt(y^2-4)` (d) `1/(2sqrt(x))sqrt(y^2+4)`

A

`(e^(sqrt(x))-e^(-sqrt(x)))/(2sqrt(x))`

B

`(e^(sqrt(x))-e^(-sqrt(x)))/(2x)`

C

`(1)/(2sqrt(x))sqrt(y^(2)-4)`

D

`(1)/(2sqrt(x))sqrt(y^(2)+4)`

Text Solution

Verified by Experts

`(dy)/(dx)=(e^(sqrt(x)))/(2sqrt(x))-(e^(-sqrt(x)))/(2sqrt(x))=(e^(sqrt(x)-)e^(-sqrt(x)))/(2sqrt(x))`
`=(sqrt((e^(sqrt(x))+e^(-sqrt(x)))^(2))-4)/(2sqrt(x))`
`=(sqrt(y^(2)-4))/(2sqrt(x))`
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CENGAGE-DIFFERENTIATION-Exercise (Multiple)
  1. If y=e^(sqrt(x))+e^(-sqrt(x)) , then (dy)/(dx)i se q u a lto (e^(sqrt...

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  2. Let y=sqrt(x+sqrt(x+sqrt(x+oo))) , (dy)/(dx) is equal to 1/(2y-1) (b) ...

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  3. "If "f(theta)=tan (sin^(-1)sqrt((2)/(3+cos 2theta)))," then "

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  4. f(x)=|x^(2)-3x|x|+2|. Then which of the following is/are true ?

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  5. Let f(x)=(sqrt(x-2sqrt(x-1)))/(sqrt(x-1)-1).x then

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  6. If x^3-2x^2y^2+5x+y-5=0a n dy(1)=1,t h e n y^(prime)(1)=4/3 (b) y^(1)...

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  7. If y=x^((logx)^log(logx)) then (dy)/(dx)=

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  8. If f(x-y), f(x) f(y), and f(x+y) are in A.P. for all x, y, and f(0) ne...

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  9. If y=cos^(-1)((2x)/(1+x^2)),t h e n(dy)/(dx)i s (-2)/(1+x^2) for all ...

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  10. f(n)(x)=e^(f(n-1)(x))" for all "n in N and f(0)(x)=x," then "(d)/(dx){...

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  11. Suppose f and g are functions having second derivatives f' and g' ever...

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  12. If y=e^(-x) cos x and yn+kny=0 where yn=(d^ny)/(dx^n) and kn are const...

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  13. If a function is represented parametrically be the equations x=(1+(lo...

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  14. If y=(x^2)/2+1/2xsqrt(x^2+1)+(log)esqrt(x+sqrt(x^2+1)) , prove that 2y...

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  15. A curve parametrically given by x=t+t^(3)" and "y=t^(2)," where "t in ...

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  16. "If "e^(sin(x^(2)+y^(3)))=tan""(y^(2))/(4)+sin^(-1)x," then y'(0) can ...

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  17. If y=e^(sqrt(x))+e^(-sqrt(x))," then "(dy)/(dx) is equal to

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  18. Let y=sqrt(x+sqrt(x+sqrt(x+...oo)))," then "(dy)/(dx) is equal to

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  19. If f(x-y), f(x) f(y), and f(x+y) are in A.P. for all x, y, and f(0) ne...

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  20. If a function is represented parametrically be the equations x=(1+(lo...

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