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

Question

1779 views around the world

You can reuse this answer
Creative Commons License

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#