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

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Answer 1 · 2016-09-16T14:38:05

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

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,

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

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

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

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