Find the derivative of the following functions
Question:

Find the derivative of the following functions (it is to be understood that abcdp, 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,

$f^{\prime}(x)=\lim _{h \rightarrow 0} \frac{f(x+h)-f(x)}{h}$

$=\lim _{h \rightarrow 0} \frac{x+h+a-x-a}{h}$

$=\lim _{h \rightarrow 0}\left(\frac{h}{h}\right)$

$=\lim _{1 \rightarrow 0}(1)$

$=1$

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