We need to find derivative of f(x) = sin (2x – 3)

Derivative of a function f(x) is given by –

f’(x) = {where h is a very small positive number}

∴ derivative of f(x) = sin (2x – 3) is given as –

f’(x) =

⇒ f’(x) =

We can’t evaluate the limits at this stage only as on putting value it will take 0/0 form. So, we need to do little modifications.

Use: sin A – sin B = 2 cos ((A + B)/2) sin ((A – B)/2)

∴ f’(x) =

⇒ f’(x) =

Using algebra of limits –

⇒ f’(x) =

Use the formula –

∴ f’(x) =

Put the value of h to evaluate the limit –

∴ f’(x) = 2 cos (2x – 3 + 0) = 2cos (2x – 3)

Hence,

Derivative of f(x) = sin (2x – 3) = 2cos (2x – 3)