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

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I solved this problem on a test and got it right, but now I don't remember how to do it. Find \[\frac{ dy }{ dx } x \cos(y)\] at the point (−1,π)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0It seems like we will have to use the product rule. Are you familiar with the product rule?

nincompoop
 one year ago
Best ResponseYou've already chosen the best response.0do you want to just get the general derivative implicitly first then add the values later

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yes. But do I keep the x as it is or do I rplacee it with 1?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@nincompoop I know the product rule

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Do you need help with implicitly deriving the left side of your equation?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I know ow to do the implicit part. This is what I did on the test (and got it correct but now it doesn't make any sense) Step 1: (1) (sin(y))y' + cos(y) (1) = 0 Step 2: sin(y) y'  cos(y) Step 3: sin(y) y' = cos(y) Step 4: \[y' = \frac{ \cos(y) }{ \sin(y) }\] In step 1 shouldn't it be + cos(y) (0) ? but I didn't write that and still got the answer correct

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0It would not be cos(y)(0) because the derivative of x is 1

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Also, of you were following the f'g +fg' you will realize that you forgot to multiply y'sin(y) by an x.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Remember that the derivative of a constant is 0

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Is this correct? cos(y) (1) + x (sin(y) y' = 0 cos(y)  x sin(y) y' = 0 cos(y) = x sin(y) y' \[y' = \frac{ \cos(y) }{ x \sin (y) }\] \[y' = \frac{ \cos(y) }{ x \sin (y) } = \frac{ \cos \pi }{ (1) \sin \pi } = \frac{ 1 }{ (1)(0) }\] Hence it is undefined

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0The math looks correct, but I do not think it would be undefined, rather it would not exist.
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