Analyze each function. Determine and specify which rule(s) you will need to differentiate (andin whatorder). Then, differentiate (showing all work). Clearly identify the use of each rule within your work.(a)f(t)=tsin(tant)(b)y=sin(xtanx)(c)f()=cos4+sec(3)(d)g(x)=sin(3x2)(2x+1)2Let's try a tricky example.(a) Consider the function y=cos4(sec(3)). How many iterations of the chain rule will you need toapply to differentiate?(b) Compute dd[cos4(sec(3))].(c) Consider y=tan(sin(cos(sec(2x-1)-3)))2. How many times would you need to use the chainrule to differentiate?(d) Don't actually differentiate this monster, but think about what the derivative would look like. Thisexample provides a demonstration of why we call it the "chain rule". In1-2 complete sentences,explain why you think we call it the chain rule.