*This preview shows
pages
1–10. Sign up
to
view the full content.*

This
** preview**
has intentionally

**sections.**

*blurred***to view the full version.**

*Sign up*This
** preview**
has intentionally

**sections.**

*blurred***to view the full version.**

*Sign up*This
** preview**
has intentionally

**sections.**

*blurred***to view the full version.**

*Sign up*This
** preview**
has intentionally

**sections.**

*blurred***to view the full version.**

*Sign up*This
** preview**
has intentionally

**sections.**

*blurred***to view the full version.**

*Sign up*
**Unformatted text preview: **Example 3 (3.5) The figure, drawn with the implicit-plotting 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 -= =- 1 cos 1 or cos dy dy y dx dx y = = DERIVATIVE OF ARCSINE FUNCTION Now, cos y 0, since /2 y /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...

View
Full
Document