- #1

player1_1_1

- 114

- 0

## Homework Statement

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]?

## Homework Equations

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

## The Attempt at a Solution

Nothing, I couldn't do anything with this, I don't know why this is count like this, please help;] thanks!