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

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

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

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To find ( \frac{dy}{dx} ) for the curve ( x = t \sin(t) ) and ( y = t^2 + 2 ), differentiate ( y ) with respect to ( x ) using the chain rule:

[ \frac{dy}{dx} = \frac{dy}{dt} \div \frac{dx}{dt} ]

[ \frac{dy}{dt} = 2t ] [ \frac{dx}{dt} = \sin(t) + t\cos(t) ]

[ \frac{dy}{dx} = \frac{2t}{\sin(t) + t\cos(t)} ]

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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