Q. 154.0( 4 Votes )

Differentiate <sp

Answer :

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


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


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


derivative of f(x) = cos (x – π/8) 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: cos A – cos B = – 2 sin ((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) = – sin (x – π/8 + 0) = – sin (x – π/8)


Hence,


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

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