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

Jul 15, 2016

typo?

#### Explanation:

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

gotta typo in there? or trick question?

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

Jul 28, 2016

$f ' \left(t\right) = 2 {e}^{2 \left({e}^{t} - 1\right) + t}$

#### Explanation:

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

Thus: $f \left(t\right) = {e}^{2 \left({e}^{t} - 1\right)}$

$f ' \left(t\right) = {e}^{2 \left({e}^{t} - 1\right)} \cdot \frac{d}{\mathrm{dt}} \left(2 \left({e}^{t} - 1\right)\right)$
(Standard Exponential and Chain rule)

$f ' \left(t\right) = {e}^{2 \left({e}^{t} - 1\right)} \cdot 2 \left({e}^{t} - 0\right)$

$f ' \left(t\right) = 2 {e}^{2 \left({e}^{t} - 1\right) + t}$