If y = e^ x + e^ x + e^ x + .... , then dy dx = - Vidyadip

MCQ

If $y = {e^{x + {e^{x + {e^{x + ....\infty }}}}}}$, then ${{dy} \over {dx}} = $

✓
${y \over {1 - y}}$
B
${1 \over {1 - y}}$
C
${y \over {1 + y}}$
D
${y \over {y - 1}}$

✓

Answer

Correct option: A.

${y \over {1 - y}}$

a
(a) $y = {e^{x + y}}$ ==> $\log y = (x + y)\log e$

==> $\frac{1}{y}\frac{{dy}}{{dx}} = 1 + \frac{{dy}}{{dx}}$

==> $ \frac{{dy}}{{dx}} = \frac{y}{1-y} $.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from STD 12 - 5. continuity and differentiation→STD 12 - 5. continuity and differentiation — all question types→Mathematics STD 12 Science question papers→CBSE Board STD 12 Science question papers→CBSE Board question paper generator→

Similar questions

Let $f(x)$ be a polynomial function such that $f(x)+f^{\prime}(x)+f^{\prime \prime}(x)=x^{5}+64$. Then, the value of $\lim _{x \rightarrow 1} \frac{f(x)}{x-1}$

Which of the following expressions are meaningful

If $\alpha$, $\beta$, $\gamma$ be the direction angles of a vector and $\cos \alpha = \frac{{14}}{{15}}$, $\cos \beta = \frac{1}{3}$ then $\cos \gamma $=

If ${e^y} + xy = e$, the ordered pair $\left( {\frac{{dy}}{{dx}},\frac{{{d^2}y}}{{d{x^2}}}} \right)$ at $x = 0$ is equal to

If $y = {(x{\cot ^3}x)^{3/2}},$ then ${{dy} \over {dx}} = $

In Graphical solution the redundant constraint is:

If $f(x) = {\sin ^2}x + {\sin ^2}\left( {x + \frac{\pi }{3}} \right) + \cos x\cos \left( {x + \frac{\pi }{3}} \right)$ and $g\left( {\frac{5}{4}} \right) = 1$, then $(gof)(x) = $

If the area of the region bounded by the curves $y^2-2 y=-x, x+y=0$ is $A$, then $8 A$ is equal to

If the system of equations $x +y + z = 6$ ; $x + 2y + 3z= 10$ ; $x + 2y + \lambda z = 0$ has a unique solution, then $\lambda $ is not equal to

If $\text{f}\text{(x)}=\sqrt{\text{x}^2-10\text{x}+25},$ then the derivative of f(x) in the intereval [0, 7] is: