MATH 111 Lecture 11: The Chain Rule

• School: Emory University
• Department: Mathematics
• Course: MATH 111
• Professor: Huanhuan Yang

Document Summary

D/dx csc x = -csc x * cot x. D/dx sec x = sec x * tan x. Definition: if g is differentiable at x and f is differentiable at g(x), then the function f= f g is defined by f(x) = f( g(x) ) is differentiable at x and: F" (x) = f" ( g(x) ) * g" (x) In leibniz notation, if y= d (u) and u= g(x) are both differentiable functions, then: Basically, when differentiating a function that can be written as f( g(x) ), the derivative of the inner function is multiplied with the derivative of the outer function. F (x) = sin x, g (x) = x2. The chain rule can be combined with any of the other rules of derivatives. Ex: (d/dx) (g (x) )n = n ( g(x) )n-1 * g" (x) The chain rule can be used to differentiate any exponential function with a base a > 0.