How do you find the derivative of #3e^ (-3/x)#?

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Answer 1 · 2016-06-29T10:38:53

#= 9/x^2 e^ (-3/x)#

#d/dx 3e^ (-3/x)#

a few thoughts first

#d/dx alpha f(x) = alpha d/dx f(x) #

and #d/dx e^{g(x)} = g'(x) e^{g(x))# by the chain rule

so here we can say that

#d/dx 3e^ (-3/x)#
#= 3 d/dx e^ (-3/x)#
#= 3 d/dx (- 3/x) e^ (-3/x)#

#= 3 d/dx (- 3x^{-1}) e^ (-3/x)#

#= 3 (-1) (- 3x^{-1-1}) e^ (-3/x)# by the power rule

#= 3 * 3x^{-2} e^ (-3/x)#

#= 9/x^2 e^ (-3/x)#