Find the #n^(th)# derivative of the function #ln(x+2)#?

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Answer 1 · 2017-08-22T12:32:02

#(d^ny)/(dx^n)=(-1)^(n-1)((n-1)!)/(x+2)^n#

As #y=ln(x+2)#

#(dy)/(dx)=1/(x+2)#

#(d^2y)/(dx^2)=-1/(x+2)^2#

#(d^3y)/(dx^3)=-(-2)/(x+2)^3=2/(x+2)^3#

#(d^4y)/(dx^4)=-6/(x+2)^4#

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#(d^ny)/(dx^n)=(-1)^(n-1)((n-1)!)/(x+2)^n#