Derivation question

Question

The function is that

$\pi(p,w_1,w_2)= p f(X_1(p,w_1,w_2), X_2(p,w_1,w_2)) -w_1X_1(p,w_1,w_2)-w_2X_2(p,w_1,w_2)$

Differentiation the profit function with respect to $w_1$

$\partial \pi/\partial w_1= p \frac{\partial f(X_1(p,w_1,w_2), X_2(p,w_1,w_2))}{\partial w_1}\frac{\partial X_1(p,w_1,w_2)}{\partial w_1 }-w_1 \frac{\partial X_1(p,w_1,w_2)}{\partial w_1}- X_1(p,w_1,w_2)- w_2\frac{\partial X_2(p,w_1,w_2)}{\partial w_1}$

This derivation is true?? If I make a mistake, please let me know in detail.

Please check my derivation.

Thank you

Answer 1

$$ {\partial\pi\over\partial w_1}= p{\partial f\over\partial X_1}{\partial X_1\over\partial w_1}+ p{\partial f\over\partial X_2}{\partial X_2\over\partial w_1}- w_1{\partial X_1\over\partial w_1}-X_1-w_2{\partial X_2\over\partial w_1} $$