Question

Find dy/dx of x cos(y) = 1 at the point (-1,pi) using implicit differentiation

Answer 1

I know that I need to use the product rule. My question is, do I keep the x as it is or do I need to replace it with -1?

Answer 2

\[\frac{ d }{ dx }\left( x \cos y \right) = \frac{ d }{ dx } (1)\]
\[\frac{ d }{ dx }(x) \cos y + x \frac{ d }{ dx }\left( \cos y \right)=0\]
\[\cos y - x \sin y \frac{ dy }{ dx }=0\]
\[\frac{ 1 }{ x }\cot y =\frac{ dy }{ dx }\]
And if we replace x=-1 and y=pi we see that dy/dx doesn't exist for (-1,pi)

Answer 3

Thanks this makes sense. But I did it totally different on a test which now doesn't make any sense, and still got it right. I posted in the mathematics section how I did it.