Answer:
[tex]\displaystyle\frac{d(y(t))}{dt} =\displaystyle\frac{d(f(u(t)))}{dt} = f'(u(t)).u'(t)[/tex]
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:
[tex]\displaystyle\frac{d(r(s(u)))}{du} = r'(g(u)).s'(u)[/tex]
Now, we are given
[tex]y(t) = f(u(t))[/tex]
Then, by chain rule, we have:
[tex]\displaystyle\frac{d(y(t))}{dt} =\displaystyle\frac{d(f(u(t)))}{dt} = f'(u(t)).u'(t)[/tex]
