Question

Q37 Consider the following given function.
y = log[(px +q) (rx + s)]
Determine the nth differential
coefficients of y.
Ops: A
(-1)n-1
(n - 1)! [(p" / (px +
(m / (rx +s)"))
q)") -
B.
(-1) n+1 (n + 1) Iron​

Answer 1

Answer:

Y=xlog(x-1/x+1) nth derivative solved - 4880352. ... Ask for details; Follow; Report ... yn = (-1)n (n-2)! (x+n)÷(x+1) n ... Hy guys. .. what is ment by bonjour in ...

Answer 2

Answer:

$\frac{d^{n}y }{dx^{n} }=(-1)^{n-1}(n-1)! [ \frac{p^{n} }{(px+q)^{n} } +\frac{r^{n} }{(rx+s)^{n} }$

Step-by-step explanation:

$y=log[(px+q)(rx+s)]$

We know that : $log(ab)=log a +logb$

Therefore $y=log(px+q)+log(rx+s)$

Differentiating these terms :

$\frac{dy}{dx} =\frac{1}{px+q} p+\frac{1}{rx+s} .r\\\\= \frac{p}{px+q}+\frac{r}{rx+s}$

Differentiating further :

$\frac{d^{2}y }{dx^{2} } = \frac{d}{dx} (\frac{p}{px+q} )+\frac{d}{dx} (\frac{r}{rx+s})$

We know that :  $\frac{d}{dx} (\frac{1}{x} )=\frac{-1}{x^{2} }$

So $\frac{d^{2} y}{dx^{2} } =\frac{-p^{2} }{px+q}+\frac{-r^{2} }{rx+s}$

Differentiating further :

$\frac{d^{3}y }{dx^{3} }=-p^{2} [\frac{-2p}{(px+q)^{3} } ]+(-r^{2} )[\frac{-2r}{(rx+s)^{2} } ]$

$\frac{d^{3}y }{dx^{3} }= (-1)^{2} *2[ \frac{p^{3}}{(px+q)^{3} } + \frac{r^{3}}{(rx+s)^{3} }]$

By continuing further, we get that the nth differential is :

$\frac{d^{n}y }{dx^{n} }=(-1)^{n-1}(n-1)! [ \frac{p^{n} }{(px+q)^{n} } +\frac{r^{n} }{(rx+s)^{n} }$