Question

find (dy/dx) when x= 1/4 when y=cos(πx)

Answer 1

when x = 1/4, y = cos (pi/4) = sqrt(2)/2

dy/dx is the derivative of cos(pi x).

The derivative of cos(pi x) using the Chain Rule is - pi sin(pi x)

So at x = 1/4, you get - pi sin(pi/4)
= - pi (sqrt 2/2) or (- pi sqrt(2)/2)