Find the derivation of each of the following from the first principle:

sin (2x + 3)

Let f(x) = sin (2x + 3)

We need to find the derivative of f(x) i.e. f’(x)

We know that,

…(i)

f(x) = sin (2x + 3)

f(x + h) = sin [2(x + h) + 3]

Putting values in (i), we get

Using the formula:

Putting h = 0, we get

= 2cos(2x + 0 + 3)

= 2cos(2x + 3)

Hence, f’(x) = 2cos (2x + 3)