questionr
Early access
Exams
Joint Entrance Examination
Mathematics
Differentiation
Question 37
Question 37 of 67
Medium
MCQ
If xloge(logex) - x2 + y2 = 4(y > 0), then \[{{dy} \over {dx}}\] at x = e is equal to :
A
\[{{\left( {1 + 2e} \right)} \over {2\sqrt {4 + {e^2}} }}\]
B
\[{{\left( {1 + 2e} \right)} \over {\sqrt {4 + {e^2}} }}\]
C
\[{{\left( {2e - 1} \right)} \over {2\sqrt {4 + {e^2}} }}\]
D
\[{e \over {\sqrt {4 + {e^2}} }}\]
Check answer
Press A-D to select · Enter to check
Solutions · 1
Post your solution
Official solution
Differentiating with respect to x, \[x.{1 \over {\ell nx}}.{1 \over x} + \ell n(\ell nx) - 2x + 2y.{{dy} \over {dx}} = 0\] at
x
=
e
x = e
x
=
e
we get \[1 - 2e + 2y{{dy} \over {dx}} = 0 \Rightarrow {{dy} \over {dx}} = {{2e - 1} \over {2y}}\] \[ \Rightarrow {{dy} \over {dx}} = {{2e - 1} \over {2\sqrt {4 + {e^2}} }}\,\,\] as \[y(e) = \sqrt {4 + {e^2}} \]
Answer the question to unlock
Previous
Next