To determine To calculate: The value of d y d x for the given equation 5 x 6 y 2 = 6 − 2 x − 6 y 2 at the given point ( 0 , 1 ) . Explanation Given: The given equation is 5 x 6 y 2 = 6 − 2 x − 6 y 2 . Also, the point is ( 0 , 1 ) . Formula used: Chain Rule: If f and g are functions and y = [ g ( x ) ] , then y ′ = f ′ [ g ( x ) ] ⋅ g ′ ( x ) provided that f ′ [ g ( x ) ] and g ′ ( x ) exists. And, Product rule, d d x [ f ( x ) g ( x ) ] = g ( x ) d d x [ f ( x ) ] + f ( x ) d d x [ g ( x ) ] Calculation: Implicit Differentiation: This differentiation is used to evaluate d y d x , when y is defined implicitly as a function of x . The differentiation is carried out in two steps: Step 1: Both the sides of the given equation is differentiated with respect to x . Since, y is the function of x , so always use the chain rule. d d x ( 5 x 6 y 2 ) = d d x ( 6 − 2 x − 6 y 2 ) 5 d d x ( x 6 y 2 ) = d d x ( 6 ) − 2 d d x ( x ) − 6 d d x ( y 2 ) 5 [ x 6 d d x ( y 2 ) + y 2 d d x </

MATH W/APPLICAT.W/NOTES GDE +ACCESS CODE

11th Edition

ISBN: 9781323751671

Author: Lial

Publisher: PEARSON C

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Chapter 12.4, Problem 24E

To determine

To calculate: The value of dydx for the given equation 5x6y2=6−2x−6y2 at the given point (0,1).

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Chapter 12.4, Problem 23E

Chapter 12.4, Problem 25E

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Chapter 12 Solutions

MATH W/APPLICAT.W/NOTES GDE +ACCESS CODE

Ch. 12.1 - Checkpoint 1 For what values of x is the function...Ch. 12.1 - Checkpoint 2 Find all intervals on which is...Ch. 12.1 - Checkpoint 3 Identity the x-values of all points...Ch. 12.1 - Checkpoint 4 Find the critical numbers for each of...Ch. 12.1 - Prob. 5CP Ch. 12.1 - Prob. 6CP Ch. 12.1 - Checkpoint 7 Find the locations of the local...Ch. 12.1 - Prob. 8CP Ch. 12.1 - Checkpoint 9 If a sales function is given by...Ch. 12.1 - Prob. 1E

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