Question

how to find the derivative of y=3tan(piex^2)

using the chain rule?

Answer 1

u = pi x^2
du/dx = 2pi x

v = tan(u)
dv/du = sec^2(u)

y = 3v
dy/dx = 3 dv/dx = 3 sec^2(u) du/dx = 6pi*x*sec^2(pi x^2)

Answer 2

Make that dv/du