Find derivative of xsin^y=siny^x

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Homework Help Overview

The discussion revolves around finding the derivative of the equation x^sin(y) = (sin(y))^x. Participants are clarifying the equation's structure and notation before proceeding with differentiation.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants are questioning the notation of the equation, particularly whether sin(y^x) or (sin y)^x is intended. There are also suggestions to take the logarithm of both sides as a potential starting point for differentiation.

Discussion Status

The discussion is ongoing, with participants actively clarifying the equation and confirming their understanding of the derivative being sought. Some guidance has been offered regarding the use of logarithmic differentiation.

Contextual Notes

There are indications of potential typos in the original problem statement, and participants are working to ensure clarity in the equation's format before proceeding with the differentiation process.

balla123
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any step by step solutions for how to find derivative of xsin^y=siny^x

it is a problem in my notes that i didnt solve yet. thanks!

edit: correct problem

x^siny = (siny)^x
 
Last edited:
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i think you have a typo...perhaps the left side of the equation should read sin x^y?
 


94JZA80 said:
i think you have a typo...perhaps the right side of the equation should read sin x^y?

i have it in my notes at siny^x

edit: but perhaps i did a type maybe?
 


also need to clarify whether siny^x means sin(y^x) or (sin y)^x. Additionally, I think something is missing on the left hand side.
 


oops sorry, i meant the left-hand side of the equation too...i'll edit my initial post to reflect that...
 


94JZA80 said:
oops sorry, i meant the left-hand side of the equation too...i'll edit my initial post to reflect that...

yes you are right..so sorry

x^siny = (siny)^x
 


By derivative, do you mean dy/dx? If so, a starting point might be to take the log of both sides. Then, proceed with implicit differentiation.
 


hotvette said:
By derivative, do you mean dy/dx? If so, a starting point might be to take the log of both sides. Then, proceed with implicit differentiation.

yes i meant dy/dx
 

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