Question

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

Answer 1

`(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))`