Problem

Differentiate

Solution

We can think of this as the composite of two functions, h(g(x)), where g(x) = (x + 2) and h(x) = x⁴.

Then we apply the chain rule:

(hog)'(x) = h'(g(x)) g'(x)

Substituting the functions h and g, we find that h'(x) = 4x³, g'(x) = 1, so

If we substitute the definition of g(x) into the composition function and expand it, we get

Applying the power rule to this function, we get

This is equal to 4(x + 2)³, the answer we get using the chain rule.