MCQ
If ${x^y} = {e^{x - y}}$, then ${{dy} \over {dx}} = $
- ✓$\log x.{[\log (ex)]^{ - 2}}$
- B$\log x.{[\log (ex)]^2}$
- C$\log x.{(\log x)^2}$
- DNone of these
==> $y = \frac{x}{{1 + \log x}}$
==> $\frac{{dy}}{{dx}} = \log x{(1 + \log x)^{ - 2}} = \log x{[\log ex]^{ - 2}}$.
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$\left|\begin{array}{lll}x+2 & x+3 & x+2 a \\ x+3 & x+4 & x+2 b \\ x+4 & x+5 & x+2 c\end{array}\right|$ is
Let $x _1< x _2< x _3<\ldots< x _{ n }<\ldots$ be all the points of local maximum of $f$ and $y_1$
$(1)$ $\left|x_n-y_n\right|>1$ for every $n$
$(2)$ $x_1 < y _1$
$(3)$ $x_n \in\left(2 n , 2 n +\frac{1}{2}\right)$ for every $n$
$(4)$ $x_{n+1}-x_n>2$ for every $n$