Double differentiation of e Power 100t+x?

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Answer 1 · 2018-06-12T04:09:11

If #f(x) = e^(100t+x)# then #f''(x) = e^(100t+x)#
[#t# assumed to be a constant]

This question is somewhat ambiguous in that we do not know the nature of #t#. Also the function could be #e^(100t) + x# or # e^(100t+x)#

I will choose the latter and take #t# to be a constant.

#:. f(x) = e^(100t+x)#

#= e^(100t) xx e^x#

Since #t# is a constant #-> e^(100t)# is also a constant.

#:. f'(x) = e^(100t) d/dx e^x#

Apply standard derivative

#f'(x) = e^(100t) e^x#

#=e^(100t+x) = f(x)#

In fact #f^n(x) = f(x)#

#:. f''(x) = e^(100t+x)#