Question

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

Answer 1

Answer:

$\displaystyle\frac{d(y(t))}{dt} =\displaystyle\frac{d(f(u(t)))}{dt} = f'(u(t)).u'(t)$

Step-by-step 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:

$\displaystyle\frac{d(r(s(u)))}{du} = r'(g(u)).s'(u)$

Now, we are given

$y(t) = f(u(t))$

Then, by chain rule, we have:

$\displaystyle\frac{d(y(t))}{dt} =\displaystyle\frac{d(f(u(t)))}{dt} = f'(u(t)).u'(t)$