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Unformatted text preview: Example 3 (3.5) The figure, drawn with the implicitplotting command of a computer algebra system, shows part of the curve sin( x + y ) = y 2 cos x . s As a check on our calculation, notice that y’ = 1 when x = y = 0 and it appears that the slope is approximately 1 at the origin. IMPLICIT DIFFERENTIATION Example 3 Find y” if x 4 + y 4 = 16. IMPLICIT DIFFERENTIATION Example 4 (3.5) Recall the definition of the arcsine function: Differentiating sin y = x implicitly with respect to x , we obtain: 1 sin means sin and 2 2 y x y x y π= =≤ ≤ 1 cos 1 or cos dy dy y dx dx y = = DERIVATIVE OF ARCSINE FUNCTION Now, cos y ≥ 0, since – π /2 ≤ y ≤ π /2. So, Thus, 2 2 cos 1 sin 1 y y x ==2 1 2 1 1 cos 1 1 (sin ) 1 dy dx y x d x dx x= ==DERIVATIVE OF ARCSINE FUNCTION Differentiate: a. b. f ( x ) = x arctan 1 1 sin y x= x Example 5 (3.5) DERIVATIVES OF ITFs...
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 Fall '08
 Noohi
 Calculus, Derivative, Implicit Differentiation, Slope, Mathematical analysis, Inverse function

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