Differentiate #d/dxe^(e^(2x))#?

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(i mean expotential power expotential power 2x)

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Answer 1 · 2017-08-15T03:10:08

#2e^((e^(2x)+2x))#

For this problem we shall use the chain rule along with the standard differential of #e^x# as follows:

#d/dx e^f(x) = e^f(x)* d/dxf(x)#

In our example #f(x) = e^(2x)#

Hence, #d/dx e^(e^(2x) )= e^(e^(2x) )* d/dx e^(2x)#

#=e^(e^(2x) )* e^(2x) *d/dx 2x#

#=e^(e^(2x) )* e^(2x) *2#

#=2e^((e^(2x)+2x))#