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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 cos 2theta=(sqrt(2)+1)(cos theta-(1)/(sqrt(2))), then the general v...

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  4. f(x)=|x^2-3|x|+2|dot 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)xdot Then f^(prime)(10=1 f...

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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"(logdotx))),t h e n(dy)/(dx)i s y/x(1n x^(oox-1)...

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  8. If f(x-y),f(x)f(y),a n df(x+y) are in A.P. for all x , y ,a n df(0)!=0...

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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. fn(x)=e^(f(n-1)(x)) for all n in Na n df0(x)=x ,t h e n d/(dx){fn(x)}...

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  11. Suppose fa n dg are functions having second derivative f" and g' ' eve...

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  12. If y=e^(-x)cosxa n dyn+kn y=0,w h e r eyn=(d^(n y))/(dx^n)a n dkn are ...

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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)i se q u a lto (e^(sqrt...

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

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  19. If f(x-y),f(x)f(y),a n df(x+y) are in A.P. for all x , y ,a n df(0)!=0...

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

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