Alright so my issue is that i get stuck at this point and do not know what i should do to isolate (dy)/(dx) since it is asking for implicit differentiation and this is what i have so far. ln(y)∗y^x∗(dy)/(dx)=ln(x)∗x^y∗(dy)/(dx)

fluerkg 2022-10-15 Answered
Alright so my issue is that i get stuck at this point and do not know what i should do to isolate d y d x since it is asking for implicit differentiation and this is what i have so far
ln ( y ) y x d y d x = ln ( x ) x y d y d x
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Answers (2)

Theresa Wade
Answered 2022-10-16 Author has 9 answers
Try first taking the logarithm of both sides.
y x = x y
x ln y = y ln x
Next derive both sides with respect to x.
d d x ( x ln y ) = d d x ( y ln x )
You'll need the product rule to continue. I'll do the LHS. Think you've got the RHS? Let me know!
ln y + x 1 y d y d x = d d x ( y ln x )
The answer ought to be equivalent to
d y d x = y x y x ln y x y ln x
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Bairaxx
Answered 2022-10-17 Author has 4 answers
Take the logs and separate.

Because y x = x y , so then ln y y = ln x x (unless x = 0 y = 0)
Now d d x ( ln x x ) = 1 ln x x 2
And you can take it from there.
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