How to prove this equation from the first attachment

[funlord]

I can's understand the fact about the equation

i can't prove the equation from the first attachment to the second attachment pls help.

Sorry for bad english

 

[andrewkirk]

The second last formula is $\frac{dx}{dy}\frac d{dx}\left(\frac{dy}{dx}\right)^{-1}$.
If we write $y'$ for $\frac{dy}{dx}$ then that is
$$\frac1{y'}\frac d{dx}\left(\frac 1{y'}\right)$$
What happens when you perform the differentiation?

 

[funlord]

Thank you very much, I can understand now why it has a negative sign