By exponents do you mean brackets? If so then it might help to know you can re-write it as

f(x) = [ sin( 1 + {cos( 1 + [tan(1+x)]^4) }^3) ]^2

and yes, the chain rule nested

Here's a few more of the pieces...

... and just in case a picture helps...

... so...

... so...

... so...

Etc...

Nesty nasty! Excuse myriad errors, hopefully fixed.

Or perhaps you meant exponents after all... loads of fun then!

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