QJEEM19Ma6857: JEE Main 2019 Mathematics - Class 12 JEEM19Ma6857 Solution: Let f be a differentiable function such that f(1) = 2 and f…

Question

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Let f be a differentiable function such that f(1) = 2 and f '(x) = f(x) for all x

\in

R R. If h(x) = f(f(x)), then h'(1) is equal to :

Accepted Answer

\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(1)) f'(1)

= f '(2) f '(1)

= 2e . 2 = 4e

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