Question

Nth derivative of ax+b/cx+d

Answer 1

nth derivative of  (a x + b) / (c x + d)

$Let\ y=\frac{ax+b}{cx+d}=\frac{a}{c}+\frac{b-\frac{ad}{c}}{cx+d}\\\\y'=\frac{dy}{dx}=\frac{bc-ad}{c}*\frac{-c}{(cx+d)^2}\\\\y''=(bc-ad)*\frac{2c}{(cx+d)^3}\\\\y^{(3)}=(bc-ad)\ (-1)^3\ 3!\ c^2\ (cx+d)^{-4}\\\\General\ formula\\\\ y^{(n)}=(-1)^n\ n!\ c^{(n-1)}\ (cx+d)^{-n}$

Answer 2

Answer:

Step-by-step explanation:

Y=ax+b/cx+d

Y=a/c+bc-bd/c(cx+d)

Yn=0+bc-ad/c.Dn(1/cx+d)

Yn=bc-ad/c.(-1^n n!c^n/(cx+d)^n+1

Yn=(-1)^n n!(bc-ad)c^n-1/(cx+d)^n+1