Question

Given y = f(u) and u = g(x), find dy/dx using Leibniz's notation for the chain rule:

a) dy/dx = dy/du * du/dx
b) dy/dx = du/dy * dy/dx
c) dy/dx = du/dx * dy/du
d) dy/dx = dx/dy * du/dx

Answer 1

The chain rule in Leibniz's notation states that dy/dx = dy/du * du/dx. To find dy/dx, find the derivatives dy/du and du/dx separately and multiply them together.

Step-by-step explanation:

The correct form of the chain rule in Leibniz's notation is:

dy/dx = dy/du * du/dx.

This means that to find dy/dx, we need to find the derivatives dy/du and du/dx individually and then multiply them together.

Here's how it works:

1. Start with the given equation y = f(u).
2. Find the derivative of y with respect to u: dy/du.
3. Next, use the equation u = g(x) to find the derivative of u with respect to x: du/dx.
4. Finally, multiply dy/du and du/dx together to get dy/dx.