InterviewSolution
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InterviewSolution
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If `y=sqrt(e^(sqrtx))`, find `(dy)/(dx)`. |
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Answer» Putting `sqrtx=t, e^(sqrtx)=e^(t)=u`, we get `y=sqrtu, u=e^(t) and t= sqrtx` `rArr(dy)/(dx)=(1)/(2)u^(-1//2)=(1)/(2sqrtu),(du)/(dt)=e^(t)and (dt)/(dx)=(1)/(2)x^(-1//2)=(1)/(2sqrtx)` `rArr(dy)/(dx)=((dy)/(du)xx(du)/(dt)xx(dt)/(dx))` `=((1)/(2sqrtu)xxe^(t)xx(1)/(2sqrtx))={(1)/(2sqrtu)xxuxx(1)/(2sqrtx)}=(sqrtu)/(4sqrtx)=(e^((1)/(2)t))/(4sqrtx)` `=(e^((1)/(2)sqrtx))/(4sqrtx)`. |
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