How to differentiate this step by step?

Question

#y=x(x+1)^10#

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Answer 1 · 2018-03-21T12:02:12

#dy/dx = (11x+1 ) (x+1)^9#

#dy/dx = d/dx(x) (x+1)^10 + x d/dx ((x+1)^10)#

#dy/dx = (x+1)^10 + x d/dx ((x+1)^10)#

Now using the chain rule:

#dy/dx = (x+1)^10 + x (10(x+1)^9 d/dx(x+1))#

#dy/dx = (x+1)^10 + 10x (x+1)^9 #

and simplifying:

#dy/dx = (x+1)^9(x+1 + 10x) #

#dy/dx = (x+1)^9(11x+1 ) #