1. Parametric Equation?

Hey, Again-- I just need a directive on how to get started. Thanks!

y’ if y=cos(sin(x2+1)-1))

should I make sin into a fraction?

Thanks...

2. Is the original question to find the derivative of y? Or is it to convert from rectangular to parametric equations?

If it is the former, then use the Chain Rule.

If it is the latter, then you can let $x = t$, and $y = \cos(\sin(t^2 + 1) - 1)$.

3. all he gave us was "y’ if y=cos(sin(x2+1)-1))" so he wants me to take the derv. of it?

4. The derivative is found through repeated use of the Chain Rule.

$\dfrac{dy}{dx} = -\sin(\sin(x^2 + 1)-1) \times \dfrac{d}{dx}\left[\sin(x^2 + 1) - 1\right]$

$= -\sin(\sin(x^2 + 1) - 1) \times \cos(x^2 + 1) \times \dfrac{d}{dx}\left[x^2 + 1\right]$

$= -\sin(\sin(x^2 + 1) - 1) \times \cos(x^2 + 1) \times 2x$