How would I answer the following question?

Question

Give an example of a situation in which a composite differentiation might be used. Give examples of functions that may be applicable and show how the relevant rates of change might be calculated.

Answer 1

Finding the derivative of a composite function is the usage of the chain rule:

d/dx of f(g(x)) = df/dg * dg/dx It you want the derivative at x = a, then df/dg is evaluated at g(a) and dg/dx at x = a.

Let's say position is given as a function of time x = f(g(t)) like 5 sin(t²) where f(g) = 5sin(g) and g(t) = t². If you wanted to find v(t) = dx/dt, you use chain rule.