When to use chain rule of differentiation ? Please give an example.f(x)=(x^3+4)^4 or f(x) = (x^2+sinx)^2

Use chain rule of differentiation
and find derivative of f(x)=(x^3+4)^4?

We'll use the chain
rule of differentiation to find the derivative of a function, that is the result of
composition of 2 or more functions.

We'll apply chain rule
to function f(x) = (x^2+sinx)^2

u(x) = x^2+sinx and v(u) =
u^2

f(x) = (vou)(x) = v(u(x)) = v(x^2+sinx) =
(x^2+sinx)^2

We'll differentiate f(x) and we'll
get:

f'(x) =
v'(u(x))*u'(x)

First, we'll differentiate v with respect to
u:

v'(u) = 2u^(2-1) =
2u

Second, we'll differentiate u with respect to
x:

u'(x) = (x^2+sin x)' = 2x + cos
x

f'(x) = 2u*(2x + cos
x)

We'll substitute u and we'll
get:

The derivative of f(x) is: f'(x) =
2(x^2+sinx)*(2x + cos x)