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):
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...
Related questions
Question
![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
)]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F418fd126-7f9b-4db4-a312-2e5f96462821%2F66fe77e9-2981-49e1-90e6-7af8292a8e20%2F269ks2rl_processed.png&w=3840&q=75)
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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