3.6Post - 3.6 Chain Rule Chain Rule [email protected] Hg HxLLD = f Hg...

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3.6 Chain Rule Chain Rule D x @ f H g H x LLD = f ¢ H g H x LL g ¢ H x L or if y = f H u L , u = g H x L then dy ÄÄÄÄÄÄÄÄ dx = dy ÄÄÄÄÄÄÄÄ du du ÄÄÄÄÄÄÄÄ dx Derivative of a Parametrically Defined Plane Curve For a parametrically defined plane curve, if x = f H t L and y = g H t L , then dy ÄÄÄÄÄÄÄÄ dx = dy ÄÄÄÄÄÄ dt ÄÄÄÄÄÄÄÄÄÄ dx ÄÄÄÄÄÄ dt = g ¢ H t L ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ f ¢ H t L For problems 1 - 8, find dy ÄÄÄÄÄÄÄÄ dx . 1. y = tan u, u = 3 x 2 2. y = "#### u 3 , u = x 2 + 5 x 3. y = - 2 x cot i k j j j j j j è!!!! x ÄÄÄÄÄÄÄÄÄÄÄÄ 3 y { z z z z z z 4. y = H 3 x 2 - x + 2 L H x 3 + 5 x L 4 5. y = csc H cot 2 x L 6. y = i k j j j 3 x + 4 ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ ÄÄÄÄÄÄÄÄ 6 x - 1 y { z z z 3 7. y = sin 3 H 2 x L "################## cos H 3 x L 8. y = cos 2 "################ 3 - 7 x
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For problems 9 - 12, find the equation of the tangent line at the given value of t. 9. x = sect, y = tan t, t = p ÄÄÄÄ 4 10. x = 3 t 2 - 6 t, y = "## t , t = 4 11. x = cos 3 t, y = sin 2 t, t = -p ÄÄÄÄÄÄÄÄ 6 12. x = t 3 + 1, y = t 2 - 2 t, t = - 2 13. Let s = csct. Find ds ÄÄÄÄÄÄÄÄ dy when t = 2 p ÄÄÄÄÄÄÄÄ 3 and dt ÄÄÄÄÄÄÄÄ
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