What's the derivative of #arctan(6^x)#?

1 Answer
Eddie
Jun 24, 2016

# y' = ( ln(6) 6^x)/( 1 + 6^{2x} )#

Explanation:

#y=arctan(6^x)#
#tan y=6^x#
#sec^2 y \ y' = (6^x)'#

#z = 6^x#
#ln z = x ln(6)#
#1/z z' = ln(6)#
#z' = ln(6) 6^x#

#\implies sec^2 y \ y' = ln(6) 6^x#

# y' = ( ln(6) 6^x)/( sec^2 y)#

using #tan^2 +1 = sec^2#

# y' = ( ln(6) 6^x)/( 1 + 6^{2x} )#

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