MathematicsIf f(x)=cosx.cos2x.cos4x.cos8x.cos16x, then f'(π4) is

If $f (x) = \cos x . \cos 2 x . \cos 4 x . \cos 8 x . \cos 16 x$ , then $f' (\frac{π}{4})$ is

$f (x) = \cos x . \cos 2 x . \cos 4 x . \cos 8 x . \cos 16 x$

$\log f (x) = logcos x + logcos 2 x + \dots + logcos 16 x$

$\frac{f' (x)}{f (x)} = - \frac{\sin x}{\cos x} - \frac{2 \sin 2 x}{\cos 2 x} - \dots - \frac{16 \sin 16 x}{\cos 16 x}$

$f' (x) = - f (x) [\tan x + 2 \tan x + \dots + 16 \tan 16 x]$

$at x = \frac{π}{4}$

$f' (\frac{π}{4}) = 0$

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