How do you find $dy/dx$ for the curve $x=t*sin(t)$ , $y=t^2+2$ ?

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Answer 1 · 2014-08-28T02:11:36

To find the derivative of a parametric function, you use the formula:

$dy/dx = (dy/dt)/(dx/dt)$ , which is a rearranged form of the chain rule.

To use this, we must first derive $y$ and $x$ separately, then place the result of $dy/dt$ over $dx/dt$ .

$y=t^2 + 2$

$dy/dt = 2t$ (Power Rule)

$x=tsin(t)$

$dx/dt = sin(t) + tcos(t)$ (Product Rule)

Placing these into our formula for the derivative of parametric equations, we have:

$dy/dx = (dy/dt)/(dx/dt) = (2t)/(sin(t)+tcos(t))$

How do you find dy/dxdy/dx for the curve x=t*sin(t)x=t*sin(t), y=t^2+2y=t^2+2 ?