CODEWITHSUNDEEP
wolfram-mathematica
Cristóbal Rodero Gómez
Cristóbal Rodero Gómez

Reputation: 15

Isolating partial derivative from an implicit equation in Mathematica

I have a basic problem in Mathematica 11.0 which has puzzled me for a while. I want to calculate y'[x] knowing that Cos[x + Sin[y]] =Sin[y]. I first calculate the derivative w.r.t. x but, when I trie to isolate the partial derivative I get an error message. The code I used is the following:

In[23]:= Dt[Cos[x + Sin[y]] == Sin[y], x]

Out[23]= sin(x+sin(y)) (-(cos(y) \[DifferentialD]y/\[DifferentialD]x + 1))==cos(y) \[DifferentialD]y/\[DifferentialD]x

In[24]:= Solve [%, \[DifferentialD]y/\[DifferentialD]x]

Error: \[DifferentialD]y/\[DifferentialD]x is not a valid variable.

I tried changing the name of \[DifferentialD]y/\[DifferentialD]x too, but it doesn't work neither.

Upvotes: 1

Views: 122

Answers (1)

Alan
Alan

Reputation: 9620

Dt[Cos[x + Sin[y]] == Sin[y], x] /. {Dt[y, x] -> dydx}
Solve[%, dydx]

Upvotes: 1

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