Question

State the chain rule for the derivative dy/dt if y(t)=f(u(t))(chain of f and u)

Answer 1

`\displaystyle(d(y(t)))/(dt) =\displaystyle(d(f(u(t))))/(dt) = f'(u(t)).u'(t)`

Explanation:

The chain rule helps us to differentiate functions and a composition of two functions.

Let r(u) and s(u) be two function. Then, composition of these two functions can be be differentiated with the help of chain rule. It states that:

`\displaystyle(d(r(s(u))))/(du) = r'(g(u)).s'(u)`

Now, we are given

`y(t) = f(u(t))`

Then, by chain rule, we have:

`\displaystyle(d(y(t)))/(dt) =\displaystyle(d(f(u(t))))/(dt) = f'(u(t)).u'(t)`