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By the 'Chain Rule'
dy/dx = dy/du X du/dx
Y = Cos (pi*x).
Let pi*x = u
Y = Cos(u)
u = pi*x
dy/du = -Sin(u)
du/dx = pi
Hence
dy/dx = dy/du X du/dx => ( Chain Rule)
dy/dx = -Sin(u) X pi
Substitute u for pi*x
Hence
dy/dx = -Sin(pi*x) X pi
Tidying up
dy/dx = -piSin(pix) Done!!!!
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