I'm having trouble figuring out where to go with this implicit differentiation problem.
Problem: Find $\frac{dy}{dx}$ given that $\sin(x)=e^{-y\cos(x)}$
Here is how I start:
- $d(\sin(x))=d(e^{-y\cos(x)})$
- $dx\cos(x)=e^{-y\cos(x)}(-dy\cos(x)+y(\sin(x)))$
Here is where I get stuck, and I've tried a lot of different manipulations. I'm not sure how to isolate $\frac{dy}{dx}$. There's no way to factor or combine like terms -that I can see- that allows one to isolate $dy$, nor $dx$, but I know of course that I'm just missing something.
Solutions with identification of relevant principle requested please.