"Given y=2sin2t and x=5cos4t, determine dy/dx."
I know I have to use the chain rule here by:
dy/dx = dy/dt x dt/dx but I'm not sure how to isolate dy/dt and dt/dx.
Please help.
There's a slightly easier way.
$\displaystyle y = 2 sin(2t)$ ==> $\displaystyle \frac{dy}{dt} = 2 cos(2t) \cdot 2 = 4 cos(2t)$
$\displaystyle x = 5 cos(4t)$ ==> $\displaystyle \frac{dx}{dt} = 5 \cdot -sin(4t) \cdot 4 = -20 sin(4t)$
Thus
$\displaystyle \frac{dy}{dx} = \frac{ \left ( \frac{dy}{dt} \right ) }{ \left ( \frac{dx}{dt} \right ) }$
$\displaystyle \frac{dy}{dx} = \frac{4 cos(2t)}{-20 sin(4t)} = - \frac{cos(2t)}{5sin(4t)}$
-Dan