Unit 3 Basic Differentiationap Calculus
Unit Guides 26 Using the Unit Guides 29 UNIT 1: Limits and Continuity 51 UNIT 2: Differentiation: Definition and Fundamental Properties 67 UNIT 3: Differentiation: Composite, Implicit, and Inverse Functions 79 UNIT 4: Contextual Applications of Differentiation 91 UNIT 5: Analytical Applications of Differentiation 109 UNIT 6: Integration. CALCULUS MAXIMUS. AP Coronavirus Calculus SCHOLARS, Tuesday, MAY 12, 2020, 1PM under a TORNADO WARNING!! Appendix: The Unit Circle. 2.3 Basic Differentiation.
Show All NotesHide All NotesSection 310 : Implicit Differentiation
For problems 1 â€“ 3 do each of the following.
 Find (y') by solving the equation for y and differentiating directly.
 Find (y') by implicit differentiation.
 Check that the derivatives in (a) and (b) are the same.
 (displaystyle frac{x}{{{y^3}}} = 1) Solution
 ({x^2} + {y^3} = 4) Solution
 ({x^2} + {y^2} = 2) Solution
For problems 4 â€“ 9 find (y') by implicit differentiation.
 (2{y^3} + 4{x^2}  y = {x^6}) Solution
 (7{y^2} + sin left( {3x} right) = 12  {y^4}) Solution
 ({{bf{e}}^x}  sin left( y right) = x) Solution
 (4{x^2}{y^7}  2x = {x^5} + 4{y^3}) Solution
 (cos left( {{x^2} + 2y} right) + x,{{bf{e}}^{{y^{,2}}}} = 1) Solution
 (tan left( {{x^2}{y^4}} right) = 3x + {y^2}) Solution
Unit 3 Basic Differentiationap Calculus 2nd Edition
Unit 3 Basic Differentiationap Calculus Calculator
For problems 10 & 11 find the equation of the tangent line at the given point.
 ({x^4} + {y^2} = 3) at (left( {1,  sqrt 2 } right)). Solution
 ({y^2}{{bf{e}}^{2x}} = 3y + {x^2}) at (left( {0,3} right)). Solution
Unit 3 Basic Differentiationap Calculus 14th Edition
For problems 12 & 13 assume that (x = xleft( t right)), (y = yleft( t right)) and (z = zleft( t right)) and differentiate the given equation with respect to t.
 ({x^2}  {y^3} + {z^4} = 1) Solution
 ({x^2}cos left( y right) = sin left( {{y^3} + 4z} right)) Solution
AP Calculus ABâ€Ž > â€Ž Unit 3: Differentiation
