Chain Rule
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Key Questions

We can do a number of things ..
1) Use the chain rule and quotient rule
2) Use the chain rule and the power rule after the following transformations.
#y=((1+x)/(1x))^3=((1+x)(1x)^1)^3=(1+x)^3(1x)^3# 3) You could multiply out everything, which takes a bunch of time, and then just use the quotient rule.
Let's keep it simple and just use the chain rule and quotient rule.
Chain Rule
#=>y'=3((1+x)/(1x))^2*((1+x)/(1x))'# #y'=3((1+x)/(1x))^2*((1x)(1)(1+x)(1))/(1x)^2# #y'=3((1+x)/(1x))^2*((1x)(1+x)(1))/(1x)^2# #y'=3((1+x)/(1x))^2*((1x)+(1+x))/(1x)^2# #y'=3((1+x)/(1x))^2*(1x+1+x)/(1x)^2# #y'=3((1+x)/(1x))^2*(1+1)/(1x)^2# #y'=3((1+x)/(1x))^2*(2)/(1x)^2# #y'=6((1+x)/(1x))^2*(1)/(1x)^2# #y'=6((1+x)^2)/(1x)^2*(1)/(1x)^2# #y'=6((1+x)^2)/(1x)^4# 
By Chain Rule and Power Rule,
#y'=1/4(x^2+3x+5)^{1/41}cdot(x^2+3x+5)'# #=1/4(x^2+3x+5)^{3/4}(2x+3)# 
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