Find dy/dx, which way should I use?

[Mamdoh Abughalion]

Homework Statement

.[/B]
Find dy/dx
Y^x = X^y

Homework Equations

F'( Ln(x)) = 1/x
Lnx^y = yLnx

The Attempt at a Solution

Ln(Y^x) = Ln(X^y)
X • Lny = Y • Lnx , should I differentiate now or :
Y = X • Lny/Lnx
Y = X • Log_xy , then differentiate ?

 

[Orodruin]

It does not matter when you differentiate as long as the equality you are differentiating is equivalent to the original one.

 

[vela]

Homework Statement

.[/B]
Find dy/dx
Y^x = X^y

Homework Equations

F'( Ln(x)) = 1/x
Lnx^y = yLnx

The Attempt at a Solution

Ln(Y^x) = Ln(X^y)
X • Lny = Y • Lnx , should I derive now or :
Y = X • Lny/Lnx
Y = X • Log_xy , then derive?

To find a derivative, you differentiate. The word derive means something else.

 

[Mamdoh Abughalion]

It does not matter when you differentiate as long as the equality you are differentiating is equivalent to the original one.

I know that , but my instructer told me that the second way is too much " dangerous " and may lead to wrong solution .

 

[LCKurtz]

Also, please don't write $F'(\ln x) = \frac 1 x$. There is no $F$. What you mean, and should write, is $(\ln x)' = \frac 1 x$ when you want to give a derivative formula.