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Here's what i got.Find the derivative for the f(x).

f(x) = pi*x + 1/(cos^2(Pi*x))

And find f'(1/4)

f'(x) = pi * d/dx (x) + d/dx (cos^2 pi*x)

^{-1}

= pi + [ (- (d/dx cos^2 (pi*x))/(cos^4(pi*x)) ]

= pi + [ (- (d/dx cos(pi*x) * (2 * cos(pi * x))/(cos^4(pi*x)) ]

= pi + [ (pi * sin x * 2cos(pi * x)) / ... ]

= pi + [ (2 * pi * sin x) / cos^3 (pi * x) ]

Thus f'(1/4) = 7.5251