burgerandcheese
Junior Member
- Joined
- Jul 2, 2018
- Messages
- 85
Hey.
I was learning about how to differentiate composite functions. This is what I read:
"If y = c(ax + b) + d.
let u = ax + b, then y = cu + d.
So dy/du = c, du/dx = a, and dy/dx = ca, that is dy/dx = dy/du * du/dx
The equation dy/du = c means that y is changing c times as fast as u; similarly u is changing a times as fast as x. It is natural to think that if y is changing c times as fast as u, and u is changing a times as fast as x, then y is changing c*a times as fast as x. Thus again, dy/dx = dy/du * du/dx"
I'm not surprised that it wasn't natural for me to think that way, and even after thinking about it, I still don't understand. I just can't get my head around it! Could somebody explain
I was learning about how to differentiate composite functions. This is what I read:
"If y = c(ax + b) + d.
let u = ax + b, then y = cu + d.
So dy/du = c, du/dx = a, and dy/dx = ca, that is dy/dx = dy/du * du/dx
The equation dy/du = c means that y is changing c times as fast as u; similarly u is changing a times as fast as x. It is natural to think that if y is changing c times as fast as u, and u is changing a times as fast as x, then y is changing c*a times as fast as x. Thus again, dy/dx = dy/du * du/dx"
I'm not surprised that it wasn't natural for me to think that way, and even after thinking about it, I still don't understand. I just can't get my head around it! Could somebody explain