17. y? = * - 1 x +1 18. x2 = *- y x + y %3D %3D

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter6: Applications Of The Derivative
Section6.CR: Chapter 6 Review
Problem 48CR
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Derivatives of Rational Pówers
Find dy/dx in Exercises 1-6.
1. y = x/4
2. y = V2x
3. y = 7Vx + 6
5. y = x(x² + 1)"2
4. y = (1 – 6x)/3
6. y = x(x² + 1)-/2
Find the first derivatives of the functions in Exercises 7–12.
7. s = V7?
9. y = sin ((2t + 5)-2/3)
11. g(x) = 2(2x¯1/2 + 1)¬1/3
8. r = Vo-3
10. f(x) = V1 – Vx
12. h(0) = V1 + cos (20)
Differentiating Implicitly
13. x²y + xy? = 6
15. x – xy + y = 1
Use implicit differentiation to find dy/dx in Exercises 13-22.
14. 2xy + y² = x + y_
16. x²(x – y)² = x² – y²
17. y² =+ 1
x- 1
x + 1
x- y
x+ y
18. x2 =
%3D
%3D
19. x = tan y
20. x + sin y = xy
()
()
21. y sin )
= 1- xy
22. y cos
= 2x + 2y
%3D
Transcribed Image Text:Derivatives of Rational Pówers Find dy/dx in Exercises 1-6. 1. y = x/4 2. y = V2x 3. y = 7Vx + 6 5. y = x(x² + 1)"2 4. y = (1 – 6x)/3 6. y = x(x² + 1)-/2 Find the first derivatives of the functions in Exercises 7–12. 7. s = V7? 9. y = sin ((2t + 5)-2/3) 11. g(x) = 2(2x¯1/2 + 1)¬1/3 8. r = Vo-3 10. f(x) = V1 – Vx 12. h(0) = V1 + cos (20) Differentiating Implicitly 13. x²y + xy? = 6 15. x – xy + y = 1 Use implicit differentiation to find dy/dx in Exercises 13-22. 14. 2xy + y² = x + y_ 16. x²(x – y)² = x² – y² 17. y² =+ 1 x- 1 x + 1 x- y x+ y 18. x2 = %3D %3D 19. x = tan y 20. x + sin y = xy () () 21. y sin ) = 1- xy 22. y cos = 2x + 2y %3D
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We do some simple algebraic manipulation then we can differentiate piecefully 

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