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What's the derivative of #arctan(8^x)#?

1 Answer

A. S. Adikesavan

Apr 15, 2016

#(8^x ln 8)/(1+8^(2x))#

Explanation:

Let u = #8^x=e^(x ln 8) and y = arc tan 8^x#.
#d/dx(y)=d/du(y)d/dx(u)#.
#=1/(1+u^2)(ln 8 e^(x ln 8))#
#= (8^x ln 8)/(1+8^(2x))#

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