Solve Q22 explaining detailly each step 16. i) Given that y+x- 2y= 0, find in terms of x and y.dxd'yii) Given that x =t'. y= 1/t, findin terms of t.dx217. Given that x =e" and y = e3, find in terms of x.dydx18. Differentiate +2ln(with respect to x and express your answer as a singlefraction19. i) Differentiate sinx with respect to x from first principledy1+3xii) Find,dxwhen a) y = (x sinx) b. y= In(1-tanz20. Find, given thatdx1-xa) y = arctan(), simplifying your answer as much as possible,b) y = In(x'-3x² + 6)?1+xc) x=y 3t + 1, leaving your answer in terms of the parameter t.21. i) Differentiate, with respect to x,In(3x2)a)b)tan( 3x -)ii) Given that y=e" + sin0, x = e" + cose finddxdywhen 0=22. Findwhen t=, where x = a(t + sint), y= a(1-cost) and a is a constant23.If y e'lnx, show that+(1 - 2y +(x-1)y 024. Given x -y = 14 y, show that (1- 2y) -2(1+()=D225. Differentiate cos0 with respect to 0 from the first principles.(26. i) differentiate, with respect to xa) cos (2Vx)In(2x)b)27. Differentiate y with respeet to x where y=cos(-3x)28. (i) Findwherea) y = Inb) x+ y+ cosxy = 0dy(ii) Given that x = e'cost and y e'sint, findwhdx54

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Answered: 22. Find when t=, where x a(t + sint),…

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Calculus

22. Find when t=, where x a(t + sint), y= a(I-cost) and a is a constant %3D

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.

Question

Solve Q22 explaining detailly each step

16. i) Given that y+x- 2y= 0, find in terms of x and y.
dx
d'y
ii) Given that x =t'. y= 1/t, find
in terms of t.
dx2
17. Given that x =e" and y = e3, find in terms of x.
dy
dx
18. Differentiate +2ln(with respect to x and express your answer as a single
fraction
19. i) Differentiate sinx with respect to x from first principle
dy
1+3x
ii) Find,
dx
when a) y = (x sinx) b. y= In(
1-tanz
20. Find, given that
dx
1-x
a) y = arctan(), simplifying your answer as much as possible,
b) y = In(x'-3x² + 6)?
1+x
c) x=y 3t + 1, leaving your answer in terms of the parameter t.
21. i) Differentiate, with respect to x,
In(3x2)
a)
b)tan( 3x -)
ii) Given that y=e" + sin0, x = e" + cose find
dx
dy
when 0=
22. Find
when t=, where x = a(t + sint), y= a(1-cost) and a is a constant
23.If y e'lnx, show that+(1 - 2y +(x-1)y 0
24. Given x -y = 14 y, show that (1- 2y) -2(1+()
=D2
25. Differentiate cos0 with respect to 0 from the first principles.(
26. i) differentiate, with respect to x
a) cos (2Vx)
In(2x)
b)
27. Differentiate y with respeet to x where y=cos(-3x)
28. (i) Find
where
a) y = In
b) x+ y+ cosxy = 0
dy
(ii) Given that x = e'cost and y e'sint, find
wh
dx
54

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