How do you differentiate f(x)=csc(ln(1ex)) using the chain rule?

1 Answer
Dec 28, 2015

Recalling the chain rule, which states that dydx=dydududvdvdx, we can rename u=ln(v) and v=1ex.

Explanation:

Doing it step-by-step, separately (which is not necessarilt advised, but this is a quite simple function, so it is ok), we'll have that f(x)=csc(u)

dydu=cscucotu

dudv=1v

dvdx=ex

Aggregating and substituting u:

dydx=csc(ln(v))cot(lnv)(1v)(ex)

Substituting v:

dydx=excsc(ln(1ex))cot(ln(1ex))1ex