What is the derivative of #x(6^(-2x))#?

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Answer 1 · 2017-04-13T01:51:26

#=(1-2xln 6)6^(-2x)#

#(x cdot 6^(-2x))'#

#=1 cdot 6^(-2x)+x cdot (6^(-2x))'#

By #(b^x)'=(ln b)b^x# and Chain Rule,

#=6^(-2x)+x cdot (ln 6)6^(-2x)(-2)#

By factoring out #6^(-2x)#,

#=(1-2xln 6)6^(-2x)#

I hope that this was clear.