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), $(x+a)$.

Answer 1

$\text{Let f(x) = x + a. Accordingly } f(x+h)=x+h+a$

$\text{By first principle,}$

f'(x)=$$\frac{f(x+h)-f(x)}{h}

$=\underset{h→0}{lim} \,\frac{x+h+-x-a}{h}$

$= \underset{h→0}{lim} \,(\frac{h}{h})$

$=\underset{h→0}{lim} \,(1)$

$=1$