Question

Express dw / dt for w=x^2 -y , x=cos(t) , y=sin(t)

Answer 1

dw/dt = -cos(t)(2sin(t) +1)

Explanation:

You want dw/dt for w = x² -y and x = cos(t), y = sin(t).

Derivative

w' = 2xx' -y' . . . . . . derivative with respect to t

w' = 2cos(t)(-sin(t)) -cos(t) . . . . . substitute given relations

dw/dt = -cos(t)(2sin(t) +1)