y = (5x² – 4x + 1)5 y = 7x - 4x y =ln (2x – 1)

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Chain Rule for differentiation
Function
Inner (u)
Outer
dy
du
dy_ dy du
(v)
du
dx
dx
du dx
y = (3x? + 5x - 5) u = 3x? + 5x – 5 y = u
y = u²
dy
(Зи") (бх + 5)
= 3x? + 5x
dx
- 5
dy
3u?
du
dy
du
= 6x + 5
dx
dx
= 3(3x + 2x
- 5)°(6x + 5)
у%3 (5x? — 4x + 1)5
y = V7x3 – 4x
у 3Dn (2х- 1)
Transcribed Image Text:Chain Rule for differentiation Function Inner (u) Outer dy du dy_ dy du (v) du dx dx du dx y = (3x? + 5x - 5) u = 3x? + 5x – 5 y = u y = u² dy (Зи") (бх + 5) = 3x? + 5x dx - 5 dy 3u? du dy du = 6x + 5 dx dx = 3(3x + 2x - 5)°(6x + 5) у%3 (5x? — 4x + 1)5 y = V7x3 – 4x у 3Dn (2х- 1)
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