*label*Mathematics

### 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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## Tutor Answer

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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