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Activity 1. Complete Me! Differentiate 2x + 2y? = 162 below by completing the table. %3D Steps Solu tion d[ d[ 1. Take the derivative of both sides with respect to x. dx dx 2. Since the left side equation is a sum of two terms, apply the Sum rule of differentiation by distributing the derivatives to d ¸ d_ dx dx dx them. 3. Perform the differentiation process. Use the Con stant multiple with Power rule of differentiation on the first tem, then use the Constant multiple with Chain rule on the second 1) + (- · a) -) term (keep in mind that whenever you are taking the derivative of the variable y the answer is ). Lastly, use Con stant rule of differentiation on the third term. dx 4. Use algebraic manipulation to isolate on one side of the equation solely and the rest to the other side (Show your algebraie manipulation/solution here) dy 5. Final an swer dx y

Activity 1. Complete Me! Differentiate 2x + 2y? = 162 below by completing the table. %3D Steps Solu tion d[ d[ 1. Take the derivative of both sides with respect to x. dx dx 2. Since the left side equation is a sum of two terms, apply the Sum rule of differentiation by distributing the derivatives to d ¸ d_ dx dx dx them. 3. Perform the differentiation process. Use the Con stant multiple with Power rule of differentiation on the first tem, then use the Constant multiple with Chain rule on the second 1) + (- · a) -) term (keep in mind that whenever you are taking the derivative of the variable y the answer is ). Lastly, use Con stant rule of differentiation on the third term. dx 4. Use algebraic manipulation to isolate on one side of the equation solely and the rest to the other side (Show your algebraie manipulation/solution here) dy 5. Final an swer dx y

Algebra and Trigonometry (MindTap Course List)
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter2: Functions
Section2.4: Average Rate Of Change Of A Function
Problem 4.2E: bThe average rate of change of the linear function f(x)=3x+5 between any two points is ________.
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Activity 1. Complete Me! Differentiate 2x2 + 2y2 = 162 below by completing the table. %3D Steps Solu tion d[ d[__] 1. Take the derivative of both sides with respect to x. dx dx 2. Since the left side equation is a sum of two tems, apply the Sum rule of differentiation by distributing the derivatives to them. d dx %3D 3. Perform the differentiation process. Use the Constant multiple with Power rule of differentiation on the first tem, then use the Constant multiple with Chain rule on the second 1)+ (-' ar) =) term (keep in mind that whenever you are taking the derivative of the variable y the answer is ). Lastly, use dx Con st ant rule of differentiation on the third term. 4. Use algebraic manipulation to isolate 2on one side of the equation solely and the rest to the other side (Show your algebraic manipulation/solution here) dy 5. Final an swer dx
Transcribed Image Text:Activity 1. Complete Me! Differentiate 2x2 + 2y2 = 162 below by completing the table. %3D Steps Solu tion d[ d[__] 1. Take the derivative of both sides with respect to x. dx dx 2. Since the left side equation is a sum of two tems, apply the Sum rule of differentiation by distributing the derivatives to them. d dx %3D 3. Perform the differentiation process. Use the Constant multiple with Power rule of differentiation on the first tem, then use the Constant multiple with Chain rule on the second 1)+ (-' ar) =) term (keep in mind that whenever you are taking the derivative of the variable y the answer is ). Lastly, use dx Con st ant rule of differentiation on the third term. 4. Use algebraic manipulation to isolate 2on one side of the equation solely and the rest to the other side (Show your algebraic manipulation/solution here) dy 5. Final an swer dx
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