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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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lenpollock

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2mo ago

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