Determine the first derivative (dy/dx) of y= tan (3x^2)
Let u = 3x^2, then
y = tan(u)
And, dy/dx = (dy/du)*(du/dx)
Taking y = tan(u), then dy/du = sec^2(u)
Taking u = 3x^2, then du/dx = 6x
So, dy/dx = (dy/du)*(du/dx)
dy/dx = (sec^2(u))*(6x)
dy/dx = 6x*sec^2(3x^2)