Multivariable Calculus: Higher-Dimensional Differentiation

[aniketvp24]

Can someone help me with what happened after changing w2? Also I am not able to understand how the epsilon 1 times epsilon 2 term came in

[BrianPulfer]

So you know that

Now, if we also modify w2 to be w2 + epsilon_2, need to apply the change not only to the first term

But also to

See this example:
If we set W_1 = w_1 + epsilon_1, and we apply the rule for w_2, we get:

But we know that:

So if we substitute it inside our previous equation we indeed get the epsilon_1 * epsilon_2 term that you see in the book.

[aniketvp24]

Thank you very much Brian! Its clear now!