Ex 1 (iii) (iv)

Dear Student
$$\begin{gathered} Let f\left(x\right)=\frac{ax+b}{cx+d} \\ Then \\ f(x+h)=\frac{a(x+h)+b}{c(c+h)+d} \\ By definition of First principal \\ {f}^{\text{'}}\left(x\right)=\underset{h\to 0}{\lim }\frac{f(x+h)-f\left(x\right)}{h} \\ =\underset{h\to 0}{\lim }\frac{{\displaystyle \frac{a(x+h)+b}{c(x+h)+d}}-{\displaystyle \frac{ax+b}{cx+d}}}{h} \\ =\underset{h\to 0}{\lim }\frac{{\displaystyle \frac{ax+ah+b}{cx+ch+d}}-{\displaystyle \frac{ax+b}{cx+d}}}{h} \\ =\underset{h\to 0}{\lim }\frac{ac{x}^2+adx+achx+adh+bcx+bd-ac{x}^2-bcx-achx-bch-adx-bd}{h(cx+ch+d)(cx+d)} \\ =\underset{h\to 0}{\lim }\frac{adh-bch}{h(cx+ch+d)(cx+d)} \\ =\underset{h\to 0}{\lim }\frac{h\left(ad-bc\right)}{h(cx+ch+d)(cx+d)} \\ =\underset{h\to 0}{\lim }\frac{ad-bc}{(cx+ch+d)(cx+d)} \\ =\frac{ad-bc}{{\left(cx+d\right)}^2} \end{gathered}$$
Kindly request you to post the other question in different thread
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