(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

problem 1

diff([f(tanx)], x) = x^2; prove that diff[f(u)]=(tan^-1(u))^2/(1+u^2)

problem 2

int(f(u), u = 0 .. 1) = f(t)-1; prove that f(a+b)=f(a)f(b) for every a,b ∈R

3. The attempt at a solution

problem 1

i don't know how to answer this question... taking the integral of f'(tan x) =x^3/3+C doesn't seem to help....

problem 2

the function seems to be the exp function where it's itself its derivative and e^0=1. but is it correct to state that the function is the exponential function directly?

btw,i'm right now learning the technique of integration.

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# Homework Help: Exponential functions with integral

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