If \[y={{x}^{{{x}^{x......\infty }}}}\], then \[\frac{dy}{dx}=\] [UPSE – McqOptions

MCQOPTIONS

1.	If \[y={{x}^{{{x}^{x......\infty }}}}\], then \[\frac{dy}{dx}=\] [UPSEAT 2004; DCE 2000]
A.	\[\frac{{{y}^{2}}}{x(1+y\log x)}\]
B.	\[\frac{{{y}^{2}}}{x(1-y\log x)}\]
C.	\[\frac{y}{x(1+y\log x)}\]
D.	\[\frac{y}{x(1-y\log x)}\]
Answer» C. \[\frac{y}{x(1+y\log x)}\]

Discussion

No Comment Found

Related MCQs

If \[y={{x}^{{{x}^{x......\infty }}}}\], then \[\frac{dy}{dx}=\] [UPSEAT 2004; DCE 2000]
If \[y={{(x\log x)}^{\log \,\log x}}\], then \[\frac{dy}{dx}=\] [Roorkee 1981]
The function \[f(x)=\frac{\text{ln}(\pi +x)}{\text{ln}(e+x)}\] is [IIT 1995]
If \[x=\sin t\] and \[y=\sin pt\], then the value of\[\left( 1-{{x}^{2}} \right)\frac{{{d}^{2}}y}{d{{x}^{2}}}-x\frac{dy}{dx}+{{p}^{2}}y\]is equal to [Pb. CET 2002]
If \[{{I}_{n}}=\frac{{{d}^{n}}}{d{{x}^{n}}}({{x}^{n}}\log x),\]then \[{{I}_{n}}-n{{I}_{n-1}}=\] [EAMCET 2003]
If a spherical balloon has a variable diameter \[3x+\frac{9}{2}\], then therate of change of its volume with respect to x is
The rate of change of \[\sqrt{({{x}^{2}}+16)}\] with respect to \[\frac{x}{x-1}\] at \[x=3\] is [AMU 2001; MP PET 1987]
If \[t=\frac{{{v}^{2}}}{2}\],then \[\left( -\frac{df}{dt} \right)\]is equal to, (where f is acceleration) [MP PET 1991]
If \[x=\sec \theta -\cos \theta \]and \[y={{\sec }^{n}}\theta -{{\cos }^{n}}\theta \], then [IIT 1989]
Let \[f(x)=\left\{ \begin{align} & {{x}^{\alpha }}\ln x,x>0 \\ & 0,\,\,\,\,\,\,\,\,\,\,\,\,x=0 \\ \end{align} \right\}\], Rolle?s theorem is applicable to f for \[x\in [0,1]\], if \[\alpha =\] [IIT Screening 2004]