ompute the derivative of f(x) = sin(x) using the definition of the d u to write out your work on paper first. (x) = lim Ar→0 f(x + ▲x) − f(x) Ax ıbstitute x + Ax into sin(x):

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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sin(x + y) = sin(x) cos(y) + cos(x) sin(y)
sin(x − y) = sin(x) cos(y) — cos(x) sin(y)
cos(x + y)
-
= cos(x) cos(y) — sin(x) sin(y)
cos(x - y) = cos(x) cos(y) + sin(x) sin(y)
Compute the derivative of f(x) = sin(x) using the definition of the derivative. For Ax, type 'deltax' with no spaces. It might be a good idea for
you to write out your work on paper first.
ƒ'(x) = _lim
Ax→0
substitute x + Ax into sin(x):
=
=
lim
Ax→0
=
ƒ(x + ▲x) − ƒ(x)
Ax
lim
Ax→0
sin(x+deltax)
apply the appropriate trig identity:
Ax
lim sin(x)
Ax→0
sin(x)
(.
Ax
+
Ax
cos(x)
I
Ax
)]
Transcribed Image Text:sin(x + y) = sin(x) cos(y) + cos(x) sin(y) sin(x − y) = sin(x) cos(y) — cos(x) sin(y) cos(x + y) - = cos(x) cos(y) — sin(x) sin(y) cos(x - y) = cos(x) cos(y) + sin(x) sin(y) Compute the derivative of f(x) = sin(x) using the definition of the derivative. For Ax, type 'deltax' with no spaces. It might be a good idea for you to write out your work on paper first. ƒ'(x) = _lim Ax→0 substitute x + Ax into sin(x): = = lim Ax→0 = ƒ(x + ▲x) − ƒ(x) Ax lim Ax→0 sin(x+deltax) apply the appropriate trig identity: Ax lim sin(x) Ax→0 sin(x) (. Ax + Ax cos(x) I Ax )]
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