If y-tan -1 loge e - x 2 loge ex2 -tan -13-2 loge x 1-6 loge x- then d 2 y d x 2-a 2b 1c 0d -1

(c) 0 y=tan 1 #160;loge #160;e/x2loge #160;ex2+tan 1 #160;3+2 #160;loge #160;x1 6 #160;loge #160;x #8658;y=tan 1 #160;1 2logex1+2logex+tan ...

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Higher Order Derivatives

If y=tan -1 l...

Question

If $y = \tan^{- 1} \{\frac{\log_{e} (e / x^{2})}{\log_{e} (e x^{2})}\} + \tan^{- 1} (\frac{3 + 2 \log_{e} x}{1 - 6 \log_{e} x})$ , then $\frac{d^{2} y}{d x^{2}} =$

(a) 2
(b) 1
(c) 0
(d) −1

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y = {tan}^{- 1} ⎡ ⎢ ⎢ ⎣ \frac{log (\frac{e}{x^{2}})}{log (e x^{2})} ⎤ ⎥ ⎥ ⎦ + {tan}^{- 1} (\frac{3 + 2 log x}{1 - 6 log x})

\frac{d^{2} y}{d x^{2}} =

y = {tan}^{- 1} ⎛ ⎜ ⎜ ⎜ ⎜ ⎝ \frac{log (\frac{e}{x^{2}})}{log (e x^{2})} ⎞ ⎟ ⎟ ⎟ ⎟ ⎠ + {tan}^{- 1} (\frac{3 + 2 log x}{1 - 6 log x})

\frac{d^{2} y}{d x^{2}}

\frac{{({log}_{e} x)}^{2} - 3 {log}_{e} x + 3}{{log}_{e} x - 1} < 1

⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩ \frac{log (\frac{e}{x^{2}})}{log (e x^{2})} ⎫ ⎪ ⎪ ⎬ ⎪ ⎪ ⎭ + {tan}^{- 1} (\frac{3 + 2 log x}{1 - 6 log x})

\frac{d^{n} y}{d x^{n}}

$L e t f : [0, \sqrt{3}] \to [0, \frac{π}{3} + l o g_{e} 2] d e f i n e d f (x) = l o g_{e} \sqrt{x^{2} + 1} + t a n^{- 1} x t h e n f (x) i s$

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