University:
University Of California, Merced
Course:
MATH 022 | Calculus II
Academic year:

2024
Views:

305

Pages:

2
Author:

Jasmyne N.

Finding Derivative With Chain Rule Chain rule is a differentiation “shortcut” to find the derivative of composite functions. A composite function is a function that contains another function as an argument. Examples: [a] sin(2x) [b] ln (3x) Notation There are 2 common types of writing the notation: [1] Lebibniz and [2] Lagrange 𝑑𝑦 𝑑𝑢 Leibniz: 𝑑𝑢 × 𝑑𝑥 Lagrange: 𝑓'(𝑔(𝑥)) × 𝑔'(𝑥) Understanding: Leibniiz: 𝑑𝑦 𝑑𝑢 refers to taking the derivative of “y” in terms of “u”. This means having an equation in terms of “u” (Ex: y = 2u) 𝑑𝑢 𝑑𝑥 refers to taking the derivative of “u” in terms of “x”. This means having a function of “u” in terms of “x” (Ex: y = 2u) Lagrange: f’(x): The first derivative of f(x) Composite Function g’(x): The first derivative of g(x) f(x) and g(x) - Solving Problem: 1. Find the derivative of f(x) = sin(3x) Leibniz Notation [1] Determine which part of the equation should be “y” and “u” [y = sin(u) and u = 3x] [2] Then solve for (dy/du) and (du/dx) [(dy/du) = cos(u) and (du/dx) = 3] [3] Substitute [f’(x) = cos(u) * 3] [4] Plug in “u” [f’(x) = cos(3x) * 3] Lagrange Notation [1] Determine the outside and inner components, label them as f(x) and g(x) [f(x) = sin(x) and g(x) = 3x] [2] Find f’(x) and g’(x) [f’(x) = cos(x) and g’(x) = 3] [3] Substitute [cos(3x) * 3] Answer: [cos(3x) * 3]

Chain Rule Notation

Related Documents

Details

Description

Related Documents

Struggling with your assignment and deadlines?

Free up your schedule!

Take 5 seconds to unlock