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B. What is the derivative of y with respect to x if y2 – x² = 4? Justine Ashley y? – x² = 4 y? = x2 + 4 y? – x² = 4 d - 4 dx d d y = Vx2 + 4 dx -y², -x² = dx' dy = (x2 + 4)2 dy 2x = 0 dx dx 2y | dy 1 (x² + 4)ż d(x² + 4) dy = 2x 2y dx dx dy 1 (x² + 4) (2x) = dy _x = - dx dx dy Vx2 + 4 y dx

B. What is the derivative of y with respect to x if y2 – x² = 4? Justine Ashley y? – x² = 4 y? = x2 + 4 y? – x² = 4 d - 4 dx d d y = Vx2 + 4 dx -y², -x² = dx' dy = (x2 + 4)2 dy 2x = 0 dx dx 2y | dy 1 (x² + 4)ż d(x² + 4) dy = 2x 2y dx dx dy 1 (x² + 4) (2x) = dy _x = - dx dx dy Vx2 + 4 y dx

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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Which of the following solution is correct? Why?

B. What is the derivative of y with respect to x if y2 - x² = 4? Justine Ashley y2 – x2 = 4 y? - x2 = 4 y? = x2 + 4 %3D d d d x2² y = Vx2 + 4 dx dy dx dx dy (x² + 4)2 2y dx - 2x = 0 dx dy 1 dy (x² + 4)² d(x² + 4) 2y 2x dx %3D dx dy 1 a² + 4) (2x) dy dx dx y dy %3D dx Vx2 + 4
Transcribed Image Text:B. What is the derivative of y with respect to x if y2 - x² = 4? Justine Ashley y2 – x2 = 4 y? - x2 = 4 y? = x2 + 4 %3D d d d x2² y = Vx2 + 4 dx dy dx dx dy (x² + 4)2 2y dx - 2x = 0 dx dy 1 dy (x² + 4)² d(x² + 4) 2y 2x dx %3D dx dy 1 a² + 4) (2x) dy dx dx y dy %3D dx Vx2 + 4
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