Answer
$\frac{dy}{dx} = - 1$
Work Step by Step
1. Find $\frac{dy}{d θ }$:
$y = cos^2θ$
**$ u = cos θ $
**$du = -sin θ dθ$
$y = u^2$
$dy = (2u)du$
$dy = 2cos θ * (-sin θ)d θ $
$dy/d θ = -2cos θ sin θ $
2. Find $\frac{dx}{d θ }$:
$x= sin^2 θ $
**$u = sin θ $
**$du = cos θ d θ $
$x = u^2$
$dx = (2u)du$
$dx = 2sin θ *(cos θ )d θ $
$\frac{dx}{d θ } = 2sin θ cos θ $
3. Using the expression: $\frac{dy}{dx} = \frac{dy/d θ }{dx/d θ }$, find the derivative:
$\frac{dy}{dx} = \frac{-2cos θ sin θ }{2sin θcos θ } = - 1$
