I find it difficult to take the derivative of something that has a constant base with a variable as an exponent...and simplify it... PLEASE HELP ME!

Question

f(x) = e^(x^(-1))

f'(x) = -1(e^(x^(-2))e^(x^(-1))

f'(x) = -e^(x^(-2))e^(x^(-1))

?????

and... f(x) = 3^x

f'(x) = 3^x

Answer 1

d/dx e^u = e^u du/dx
here u = x^-1
du/dx = -1 x^-2
so
d/dx e^(x^-1) = -x^-2 e^(x^-1)
= -(1/x^2)e^(1/x^2)
Try the others using that recipe:
d/dx e^u = e^u du/dx

Answer 2

WOW that actually helps a lot and less confusing to solve! Thanks so much!