Math 1a Spring 2020
1a Introduction to Calculus
The pain rule
The chain rule is fantastic. Avoiding it is the Pain rule.
In one of the homework, you had to compute the derivative of (1+x^{2} + x^{4})^{100}.
Foiling things out gives a polynomial but is painful as the Mathematica output of
(1+x^2+x^4)^(100)illustrates. The derivative is simply 100 (1+x^{2}+x^{4})^{99} (2x+4x^{3}). |