Question:medium
If \(f_n(x) = e^{f_{n-1}(x)}\) for all \(n \in \mathbb{N}\) and \(f_0(x) = x\) then \(\frac{d}{dx}\{f_n(x)\}\) is equal to
If \(f_n(x) = e^{f_{n-1}(x)}\) for all \(n \in \mathbb{N}\) and \(f_0(x) = x\) then \(\frac{d}{dx}\{f_n(x)\}\) is equal to
Show Hint
Derivative of \(e^{g(x)} = e^{g(x)} \cdot g'(x)\).
Updated On: Apr 7, 2026
- \(f_n(x) f_{n-1}(x) dx\)
- \(f_n(x) \frac{d}{dx}\{f_{n+1}(x)\}\)
- \(f_n(x) \cdot f_{n-1}(x) \cdot \ldots \cdot f_2(x) \cdot f_1(x)\)
- None of the above
Show Solution
The Correct Option is C
Solution and Explanation
Was this answer helpful?
0
Top Questions on Continuity
- Let $[t]$ denote the greatest integer less than or equal to $t$.
If the function
\[ f(x)= \begin{cases} b^2 \sin\!\left[\dfrac{\pi}{2}\left[\dfrac{\pi}{2}(\cos x+\sin x)\cos x\right]\right], & x < 0 \\ \dfrac{\sin x-\dfrac{1}{2}\sin 2x}{x^3}, & x > 0 \\ a, & x = 0 \end{cases} \] is continuous at $x=0$, then $a^2+b^2$ is equal to
- JEE Main - 2026
- Mathematics
- Continuity
Let
be a continuous function at $x=0$, then the value of $(a^2+b^2)$ is (where $[\ ]$ denotes greatest integer function).
- JEE Main - 2026
- Mathematics
- Continuity
Let
be a continuous function at $x=0$, then the value of $(a^2+b^2)$ is (where $[\ ]$ denotes greatest integer function).
- JEE Main - 2026
- Mathematics
- Continuity
- If \[ f(x) = \begin{cases} \frac{\sin^2(ax)}{x^2}, & x \neq 0 \\ 1, & x = 0 \end{cases} \] is continuous at \( x = 0 \), then the value of \( a \) is:
- CBSE Class XII - 2025
- Mathematics
- Continuity
- Want to practice more? Try solving extra ecology questions todayView All Questions
