How do you differentiate $f (x) = e^{2 (e^{t} - 1)}$ $f(x) = e ^ (2(e^(t) - 1)$ ?

Question

3085 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-07-15T11:10:24

typo?

$f (x) = e^{2 (e^{t} - 1)}$ $f(color{blue}{x}) = e ^ (2(e^(color{red}{t}) - 1)$

gotta typo in there? or trick question?

the trick with exponents is: $\frac{d}{d u} (e^{f (u)}) = \frac{d f}{d u} e^{f (u)}$ $d/(du) ( e^(f(u)) )= (df)/(du) e^(f(u))$

Answer 2 · 2016-07-28T13:26:32

$f'(t) = 2e^(2(e^t-1)+t)$

We will assume that the function was meant to be $f(t)$ rather than $f(x)$

Thus: $f(t) = e^(2(e^t-1))$

$f'(t) = e^(2(e^t-1)) * d/dt (2(e^t-1))$
(Standard Exponential and Chain rule)

$f'(t) = e^(2(e^t-1)) * 2(e^t - 0)$

$f'(t) = 2e^(2(e^t-1)+t)$

How do you differentiate f(x) = e ^ (2(e^(t) - 1)f(x)=e2(et−1)f(x) = e ^ (2(e^(t) - 1)?