Find slope of parametric equation

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I am looking for the slope of the parametric equation:

$$x=e^{3t}-2e^{-3t}$$ $$y=e^{3t}+5e^{-3t}$$

Find slope when $t=2$.

As of now I have figured the slope of $\frac{dy}{dx}$ to be:

$$\frac{e^{12}-5}{e^{12}-2}$$

at $t=2$ however I think I went about this problem the wrong way. To explain how I came to that slope is I calculated the derivative of y over the derivative of x and simplified.

Could someone tell me if I went about this the wrong way?

EDIT: Also I don't know if this is relevant to the problem, but I found a point at:

($e^6-2e^{-6}$ , $e^6-5e^{-6}$) at t=2.

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1 Answer

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Use $$\frac{dy}{dx}=\frac{\frac{dy}{dt}}{\frac{dx}{dt}}$$

Now, $\displaystyle y=e^{3t}-2e^{-3t}\implies \frac{dy}{dt}=3e^{3t}-2\cdot(-3e^{-3t})=3(e^{3t}+2e^{-3t})$

Similarly, find $\displaystyle \frac{dx}{dt}$

Finally divide and put $t=2$

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