If $x = {e^{y + {e^{y + {e^{\,y + \,...\,\,{\text{to}}\,\infty }}}}}},$ $x > 0,$ then $\frac{{dy}}{{dx}},$ is

JEE MATHEMATICS MCQ: DIFFERENTIATION

1 Easy

1 of 1

Analyzing +4 | -1

x = {e^{y + {e^{y + {e^{\,y + \,...\,\,{\text{to}}\,\infty }}}}}},

x > 0,

then

\frac{{dy}}{{dx}},

View answer and explanation

Correct option: C

\frac{1-x}{x}

Option C (

\frac{1-x}{x}

) is correct because it is derived by taking the logarithm of the given equation and then differentiating with respect to x.

Practice All Chapter MCQs →

f(x)=|x|^{|\tan x|}

f^{\prime}\left(\frac{-\pi}{6}\right)

x

y

x>0

x y=1

x+y

f(x)=[x] \sin (\pi x)

[x]

x

x=k, k

f(x)

y = {\sec ^{ - 1}}\left[ {\mathrm{cosec}x} \right] + \mathrm{cose}{\mathrm{c}^{ - 1}}\left[ {\sec x} \right] + {\sin ^{ - 1}}[\cos x] + {\cos ^{ - 1}}[\sin x],

\frac{{dy}}{{dx}}

\frac{d}{d x} \sin ^{-1}\left(3 x-4 x^{3}\right)

z = y + f\left( v \right),

v = \left( {\frac{x}{y}} \right),

v\frac{{\partial z}}{{\partial x}} + \frac{{\partial z}}{{\partial y}}