Prove the formula for (cos(x)) by by implicit differentiation. dx Let y = cos ¹(x). Then cos(y) =-sin(y) O syst → - sin(y) = 1 dx dy dx 1 sin(y) == ⇒ 1 and 1 - cos² sec²(x) 1-

Calculus: Early Transcendentals
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ISBN:9781285741550
Author:James Stewart
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Chapter1: Functions And Models
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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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d
- (+) (COS¯¹ (x)
dx
Prove the formula for
Let y = cos ¹(x). Then cos(y)
0 ≤ y≤ π
dy
dx
(cos(x)) by by implicit differentiation.
1
sin(y)
=
-sin(y)
dy
→ - sin(y) = 1
dx
→
1
and
1 - cos² sec²(x)
1
1-x²
Transcribed Image Text:d - (+) (COS¯¹ (x) dx Prove the formula for Let y = cos ¹(x). Then cos(y) 0 ≤ y≤ π dy dx (cos(x)) by by implicit differentiation. 1 sin(y) = -sin(y) dy → - sin(y) = 1 dx → 1 and 1 - cos² sec²(x) 1 1-x²
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