derivatives function

Question

Find  at  if  and .

Answer 1

I think that a nice way to think about this is to think of the chain rule as:

You can consider that the "dx's" just cancel out.

That means you can use standard algebra techniques to divide both sides by dy/dx so that you get:

Use the power rule to find dy/dx

dy/dx = 6x

So at x = 1, dy/dx = 6

Since you are given dy/dt = 4 then dx/dt = 4/6 or dx/dt = 2/3