Calculus 2 Homework

Anonymous

Question Description

i need someone to solve these problem in word file. so please solve each problem step by step and then show the final results. look at the file down you can see the problems.

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School: Carnegie Mellon University

hello, thanks for the patience.

CALCULUS 2

1

Calculus 2
Student’s Name
Instructor’s Name
Institutional Affiliation

CALCULUS 2

2
Calculus 2

1. Find y”
y=1/5tan(10x-5)
y’=
d/dx[tan(10x−5)]
= (1/5) sec2(10x−5)⋅d/dx[10x−5]
= (1/5) (10⋅dy/dx[x]+dy/dx [−5]) sec2(10x−5)
= (1/5) (10⋅1+0) sec2(10x−5)
=(1/5)10sec2(10x−5)
=2sec2(10x−5)
y” =
d/dx[10sec2(10x−5)]
=10⋅d/dx[sec2(10x−5)]
=10⋅2sec(10x−5) ⋅d/dx[sec(10x−5)]
=20sec(10x−5) tan(10x−5) ⋅d/dx[10x−5] ⋅sec(10x−5)
=20(10⋅d/dx[x]+d/dx [−5]) sec2(10x−5) tan(10x−5)
=20(10⋅1+0) sec2(10x−5) tan(10x−5)
=40sec2(10x−5) tan(10x−5)
2. dy/dx (3√(5x+1) (x+4)2x3+6(x+8)
(x + 4)2/3∛ 5x + 1 ∛ x3 + 6(x + 8)
((x^3+6*(x+8))^(1/3)*((2*(5*x+1)^(1/3))/(3*(x+4)^(1/3))+(5*(x+4)^(2/3))/(3*(5*x+
1)^(2/3)))((x+4)^(2/3)*(5*x+1)^(1/3)*(3*x^2+6))/(3*(x^3+6*(x+8))^(2/3)))/(x^3+6*(x+8))^(2/
3)
simplify:

CALCULUS 2

3

(2*(5*x+1)^(1/3))/(3*(x+4)^(1/3)*(x^3+6*(x+8))^(1/3))+(5*(x+4)^(2/3))/(3*(5*x+1)
^(2/3)*(x^3+6*(x+8))^(1/3))((x+4)^(2/3)*(5*x+1)^(1/3)*(3*x^2+6))/(3*(x^3+6*(x+8))^(4/3))

-(41*x^3-48*x^2-726*x-1032)/(3*root(3,x+4)*(5*x+1)^(2/3)
*(x^3+6*(x+8))^(4/3))
3. dy/dx[(x+2). sin(x)]
= (x+2) ^sin...

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