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

College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter5: Polynomial And Rational Functions
Section: Chapter Questions
Problem 27PT: Find the unknown value. 27. y varies jointly with x and the cube root of 2. If when x=2 and...
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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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