What is the derivative of #y=ln sqrt(x+1)^5/sqrt(x+2)^20#?

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Answer 1 · 2017-12-14T11:22:44

#y'=5/[(2x+2)*(x+2)^10]-(25Ln(x+1))/(x+2)^11#

#y=Ln(sqrt(x+1)^5)/(sqrt(x+2)^20)#

=#5/2Ln(x+1)/(x+2)^10#

#y*(x+2)^10=5/2*Ln(x+1)#

#y'(x+2)^10+10y*(x+2)^9=5/(2x+2)#

#y'(x+2)^10=5/(2x+2)-10y*(x+2)^9#

#y'=5/[(2x+2)*(x+2)^10]-(10y)/(x+2)#

#y'=5/[(2x+2)*(x+2)^10]-10/(x+2)*5/2Ln(x+1)/(x+2)^10#

#y'=5/[(2x+2)*(x+2)^10]-(25Ln(x+1))/(x+2)^11#