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

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

\(\text{By first principle,}\)

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

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

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

\(=\underset{h→0}{lim} \,(1)\)

\(=1\)