Find the derivative of the following -it is to be understood that a- b- c- d- p- q- r and s are fixed non-zero constants and m and n are integers- - displaystyle frac-ax-b-cx-d-

Question

Toppr Admin · Accepted Answer

Let-xA0- f-x-ax-bcx-dThus using quotient rule-f-x2032-x-cx-d-d-ax-b-dx-x2212-ax-b-d-cx-d-dx-cx-d-2-a-cx-d-x2212-c-ax-b-cx-d-2-ad-x2212-bc-cx-d-2

Find the derivative of the following function (it is to be understood that $a, b, c, d, p, q, r$ and $s$ are fixed non-zero constants and $m$ and $n$ are integers) : $\frac{a x + b}{c x + d}$

Let, $f (x) = \frac{a x + b}{c x + d}$
Thus using quotient rule,
$f^{'} (x) = \frac{(c x + d) \frac{d (a x + b)}{d x} - (a x + b) \frac{d (c x + d)}{d x}}{(c x + d)^{2}}$
$= \frac{a (c x + d) - c (a x + b)}{(c x + d)^{2}} = \frac{a d - b c}{(c x + d)^{2}}$

Find the derivative of the following function (it is to be understood that a,b,c,d,p,q,r and s are fixed non-zero constants and m and n are integers) : ax+bcx+d

Let, f(x)=ax+bcx+dThus using quotient rule,f′(x)=(cx+d)d(ax+b)dx−(ax+b)d(cx+d)dx(cx+d)2=a(cx+d)−c(ax+b)(cx+d)2=ad−bc(cx+d)2

Find the derivative of the following function (it is to be understood that $a, b, c, d, p, q, r$ and $s$ are fixed non-zero constants and $m$ and $n$ are integers) : $\frac{a x + b}{c x + d}$

Let, $f (x) = \frac{a x + b}{c x + d}$
Thus using quotient rule,
$f^{'} (x) = \frac{(c x + d) \frac{d (a x + b)}{d x} - (a x + b) \frac{d (c x + d)}{d x}}{(c x + d)^{2}}$
$= \frac{a (c x + d) - c (a x + b)}{(c x + d)^{2}} = \frac{a d - b c}{(c x + d)^{2}}$