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How do you differentiate #y = ln ((x^2+1)^5 / sqrt(1-x)) #?

1 Answer

A. S. Adikesavan

Sep 16, 2016

#(1+20x-19x^2)/(2(1-x+x^2+x^3))#

Explanation:

Using #ln(a^n)=nln a and ln(a/b)=lna-ln b and (ln u)'=1/u u'#

#y'=5 ln ( 1 + x^2 )-1/2 ln(1- x)#. So,

#y'=5/(1+x^2)(1+x^2)'-(1/2)1/(1-x)(1-x)'#

#=(10x)/(1+x^2)+1/(2(1-x))#

#=(1+20x-19x^2)/(2(1-x+x^2+x^3))#

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