Find derivative of xsin^y=siny^x

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SUMMARY

The discussion focuses on finding the derivative of the equation x^sin(y) = (sin(y))^x. Participants clarify potential typographical errors in the equation and confirm that the derivative sought is dy/dx. The recommended approach involves taking the logarithm of both sides of the equation, followed by implicit differentiation to solve for dy/dx. This method is essential for handling equations where both variables are interdependent.

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  • Basic calculus concepts, including derivatives
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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
 
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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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