Find 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): sin (x + a)

Explanation

Let `f(x)=sin(x+a)`

Thus using first principle

`f′(x)=lim_(xto0)(f(x+h)−f(x))/h`

`lim_(xto0)(sin(x+h+a)−sin(x+a))/h`

`lim_(xto0) 1/h[2cos((x+h+a+x+a)/2) sin((x+h+a−x−a)/2)]`

`lim_(xto0) 1/h[2cos((2x+2a+h)/2) sin((h)/2)]`

`lim_(xto0) [cos((2x+2a+h)/2) (sin((h)/2))/(h/2)]`

`lim_(xto0) cos((2x+2a+h)/2) lim_(xto0)(sin((h)/2))/(h/2)​`

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