I need help taking the following derivatives:
d/dt of (e^-2)*(e^(1+e^x))*(e^t)
and
d/dt of (e^-2)*(e^(1+e^t))*(e^x)
thanks
Fred1956
If $\displaystyle x \neq f(t)$ let $\displaystyle u = e^{-2}(e^{1+e^x}) $ which is a constant which gives:
$\displaystyle \frac{d}{dt}(ue^t)$ where u is a constant, should be easy enough.
$\displaystyle \frac{d}{dt}(e^{-2}e^x)(e^{1+e^t})$d/dt of (e^-2)*(e^(1+e^t))*(e^x)
Let $\displaystyle y = (e^{-2}e^x)(e^{1+e^t})$
take logs:
Spoiler:
$\displaystyle ln(y) = e^t+x-1$
Differentiate implicitly:
$\displaystyle \frac{1}{y} \frac{dy}{dt} = e^t$
$\displaystyle
\frac{dy}{dt} = ye^t = e^t(e^{-2}e^x)(e^{1+e^t})$