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)