Question:
Find the derivative of the following functions (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): (x + a)
Solution:
Let $f(x)=x+a$. Accordingly, $f(x+h)=x+h+a$
By first principle,
$f^{\prime}(x)=\lim _{h \rightarrow 0} \frac{f(x+h)-f(x)}{h}$
$=\lim _{h \rightarrow 0} \frac{x+h+a-x-a}{h}$
$=\lim _{h \rightarrow 0}\left(\frac{h}{h}\right)$
$=\lim _{1 \rightarrow 0}(1)$
$=1$