Find derivative of xsin^y=siny^x

[balla123]

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

 

[94JZA80]

i think you have a typo...perhaps the left side of the equation should read sin x^y?

 

[balla123]

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?

 

[hotvette]

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.

 

[94JZA80]

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

 

[balla123]

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

 

[hotvette]

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.

 

[balla123]

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