According to my calculus professor and MIT open coursework, taking the derivative of (x^2+4)^-1 is an application of the chain rule, not the power rule. The answer to the question is -(x^2+4)^-2, which makes sense to me, but I just don't understand why this is considered an application of the chain rule rather than the power rule, since the power rule says that d/dx(x^n) = nx^(n-1).
Here is a link to the MIT coursework I am talking about: https://ocw.mit.edu/courses/mathematics/18-01sc-single-variable-calculus-fall-2010/1.-differentiation/part-a-definition-and-basic-rules/session-11-chain-rule/MIT18_01SCF10_ex11sol.pdf
Best Answer
The derivative is $-2x(x^2+4)^{-2}$. Thus the chain rule. You missed $2x$.