Question

what is the derivative of y=4secx^2=3cotx ?

Answer 1

Is the second = supposed to be a minus? In other words, is the function
y = 4secx^2 -3cotx ?
Also, do you mean (secx)^2, or sec(x^2) ?

Answer 2

Sorry about that. y=4sec(x^2)-3cotx

Answer 3

The derivative of secx is tanx*secx.
The derivative of cotx is -csc^2x

Treat sec*(x^2) as a function f of a function g(x). f(g) = sec g; g(x) = x^2
d/dx[sec(g(x))]= d/dg(secg)*dg/x
d/dx[sec(x^2)] = tanx^2)*sec(x^2)*2x

Now add them all up, and include the constant coefficients

dy/dx = 8x tan(x^2)*sec(x^2) + 3csc^2 x