Chain Rule Application Sequence

Differentiate $f(x)=\cos(\ln(x^2+1))$ using the chain rule. Rank the following steps from outermost to innermost:
A: Differentiate the outer function, noting that $\frac{d}{du}[\cos(u)] = -\sin(u)$.
B: Identify the inner function as $u = \ln(x^2+1)$.
C: Differentiate the inner function to obtain $\frac{2*x}{x^2+1}$.
D: Multiply the results to obtain the final derivative $-\frac{2*x*sin(\ln(x^2+1))}{x^2+1}$.