Right from 10th, my teachers gave me all the formulas and techniques on how to solve problems in calculus.
Product rule= $$\frac{d}{dx}f(x)g(x)= f(x)g'(x)+g(x)f'(x)$$
Chain rule= $$\frac{dy}{dx}=\frac{dy}{du}* \frac{du}{dx}$$
Why is it that while applying product rule, one function is kept constant, while the other differentiated?
I saw the video on the visual representation of the chain rule and product rule on 3Blue1Brown, yet I'm unable to formulate an explanation for it. Especially when we increase the number of functions and variables.
I would really appreciate any help regarding this. Thanks in advance!!
Best Answer
I like to think about how the area of a rectangle changes when we vary the sides:
$$(a+\delta_a)(b+\delta_b)-ab=\delta_a b+a\delta_b+\text{ something too small to worry about.}$$