1. Tardigrade
  2. Question
  3. Mathematics
  4. Let f be a differentiable function such that f(1) = 2 and f '(x) = f(x) for all x ∈ R. If h(x) = f(f(x)), then h'(1) is equal to :

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. Let $f$ be a differentiable function such that $f(1) = 2$ and $f '(x) = f(x)$ for all $x \in R$. If $h(x) = f(f(x))$, then $h'(1)$ is equal to :

JEE MainJEE Main 2019Continuity and Differentiability

Solution:

$\frac{f'(x)}{f(x)} \, \, = \, 1 \forall \, x \in R$
Intergrate & use $f(1) = 2$
f(x) = 2e$^{x-1} \, \Rightarrow \, \, f'(x) \, = \, 2e^{x-1}$
$h(x) \, = \, f(f(x)) \Rightarrow \, h'x) \, = \, f'(f(x)) \, f'(x)$
$h'(1) \, = \, f'(f(f)) \, f'(1)$
$ \, \, \, \, = f'(2) \, f'(1)$
$=2e .2 =4e$