Thomas' Calculus Early Transcendentals (Single Variable, Chs. 1-11)Addison Wesley, 2005 - 984 oldal |
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191. oldal
... Chain Rule An object moves along the x - axis so that its position at any time t≥ 0 is given by x ( t ) = cos ( t2 + 1 ) . Find the velocity of the object as a function of t . Solution We know ... Chain Rule and Parametric Equations 191.
... Chain Rule An object moves along the x - axis so that its position at any time t≥ 0 is given by x ( t ) = cos ( t2 + 1 ) . Find the velocity of the object as a function of t . Solution We know ... Chain Rule and Parametric Equations 191.
192. oldal
... Chain Rule , we get dy d d = dx dx ( ecos x ) = e cos x ( cos x ) dx = ecos x ( -sin x ) = -ecosx sin x . Generalizing Example 5 , we see that the Chain Rule gives the formula Thus , for example , d du eu = eu dx dx d dx ( ekx ) = ekx ...
... Chain Rule , we get dy d d = dx dx ( ecos x ) = e cos x ( cos x ) dx = ecos x ( -sin x ) = -ecosx sin x . Generalizing Example 5 , we see that the Chain Rule gives the formula Thus , for example , d du eu = eu dx dx d dx ( ekx ) = ekx ...
193. oldal
... Chain Rule to extend this to the Power Chain Rule : d un = nu " - n - 1 du d dx dx du ( u ” ) = nu " ! Applying the Power Chain Rule EXAMPLE 7 d ( a ) ( 5x3 − x4 ) 7 = 7 ( 5x3 - x4 ) 6 ( 5x3- x4 ) dx Power Chain Rule with u = 5x3- x + ...
... Chain Rule to extend this to the Power Chain Rule : d un = nu " - n - 1 du d dx dx du ( u ” ) = nu " ! Applying the Power Chain Rule EXAMPLE 7 d ( a ) ( 5x3 − x4 ) 7 = 7 ( 5x3 - x4 ) 6 ( 5x3- x4 ) dx Power Chain Rule with u = 5x3- x + ...
Tartalomjegyzék
Limits and Continuity | 67 |
Differentiation | 144 |
Applications of Derivatives | 264 |
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