How do you use the chain rule to differentiate #tan(ln(4x))#?

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Answer 1 · 2017-12-27T02:43:38

#sec^2(ln(4x))/x#

Simply break it down piece by piece:

#y = tan(ln(4x))#

First differentiate the outermost function (the tan function) and apply the chain rule:

#-> dy/dx = sec^2(ln(4x)). d/dxln(4x) #

Now differentiate the #ln(4x)# and keep going:

#dy/dx = sec^2(ln(4x))1/(4x).d/dx(4x)#

#= sec^2(ln(4x))1/(4x).4=sec^2(ln(4x))/x#