Question

Differentiate the following from first principle.

sin (x + 1)

Answer 1

We need to find derivative of f(x) = sin (x + 1)

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

{where h is a very small positive number}

∴ derivative of f(x) = sin (x + 1) is given as –

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)