Question

what is the derivative of te^-t/2

Answer 1

te^(-t/2)

the derivative of

f(x) = e^u
f'(x) = (e^u)u'

Product rule is

d(x) = f(x)g(x)
d'(x) = f'(x)g(x) + g'(x)f(x)

split the problem in to smaller functions.

so find the derivative of
t
then find the derivative of
e^(-t/2)

then apply product rule

Answer 2

pretend
f(x) = e^(-t/2)
and
g(x) = t

then just take the derivative of these two functions and sub that into the product rule