Explanation of derivative - chain rule

[salves]

Hello,
This is not an exercise, but rather something I don't understand in an economics book.
k(t)=K(t)/A(t)L(t)

I don't understand this step:

We can use the chain rule to find: 

k(t)/dt= K(t)/dt x 1/(A(t)L(t)) - K(t)/(A(t)L(t))^2 x [A(t)dL(t)/dt + L(t)dA(t)/dt]

I am not sure it is very readable. Can we use latex in this forum?

Thank you!

 

[stapel]

k(t)=K(t)/A(t)L(t)

I don't understand this step:

We can use the chain rule to find: 

k(t)/dt= K(t)/dt x 1/(A(t)L(t)) - K(t)/(A(t)L(t))^2 x [A(t)dL(t)/dt + L(t)dA(t)/dt]

What did you get, when you applied the Quotient Rule to the right-hand side?

 

[salves]

Thank you so much! I don't know how I didn't get it! Since they said "chain rule" I was thinking of f(g(x))=... and was completely lost!