(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I have John R Taylor "Classical mechanics" part 1, and I have an integral:

[tex]\int\limits^{x_2}_{x_1}f\left(y+\alpha\eta,y^{\prime}+\alpha\eta^{\prime},x\right)\mbox{d}x[/tex]

and here is count derivative of underintegral function in [tex]\alpha[/tex]

[tex]\frac{\partial f\left(y+\alpha\eta,y^{\prime}+\alpha\eta^{\prime},x\right)}{\partial\alpha}=\eta\frac{\partial f}{\partial y}+\eta^{\prime}\frac{\partial f}{\partial y^{\prime}}[/tex]

why there is suddenly [tex]\frac{\partial f}{\partial y^{\prime}}[/tex] and [tex]\frac{\partial f}{\partial y}[/tex], while this derivative is by [tex]\alpha[/tex] - why not only [tex]\eta,\eta^{\prime}[/tex]?

2. Relevant equations

I was thinking about function composition derivative, but it didnt helped me.

3. The attempt at a solution

Nothing, I couldnt do anything with this, I dont know why this is count like this, please help;] thanks!

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Partial derivative - why is it count like this?

**Physics Forums | Science Articles, Homework Help, Discussion**