Question

Differentiate the following from first principle.

cos(x - π/8)

Answer 1

We need to find derivative of f(x) = cos (x – π/8)

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

{where h is a very small positive number}

∴ derivative of f(x) = cos (x – π/8) 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: cos A – cos B = – 2 sin ((A + B)/2) sin ((A – B)/2)

Put the value of h to evaluate the limit –

∴ f’(x) = – sin (x – π/8 + 0) = – sin (x – π/8)

Hence,

Derivative of f(x) = cos (x – π/8) = – sin (x – π/8)