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masha68 [24]
2 years ago
14

What is the domain and derivative of f(x)=ln(2xsqrt(2+x))?

Mathematics
1 answer:
harkovskaia [24]2 years ago
7 0
Domain is the numbers yo can use
we has a sqrt and a ln
we cant have any neagtive ln's or sqrts
x cannot be negative
it cannot be 0 either
domain is all numbers bigger than 0


deritivive
apply chain rule
dy/dx(f(g(x))=f'(g(x))g'(x)
and also
dy/dx (lnx)=1/x
and
dy/dx(f(x)g(x))=f'(x)g(x)+g'(x)f(x)
and from experience
dy/dx(sqrtx)=1/(2√x)


so

dy/dx(ln(2xsqrt(2+x)))=
(1/(2xsqrt(2+x))(2)(sqrt(2+x)+(x/(2sqrt(2+x))=
(3x+4)/(2x(x+2))



domain is all real numbers greater than 0
derivitive is \frac{3x+4}{2x(x+2)}
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Steps to solve:

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~Distribute left side

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Step-by-step explanation:

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3 years ago
The sum of two numbers is 90. Their difference is 18. Find<br> the numbers.
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Answer:

36 & 54

Step-by-step explanation:

<em><u>By </u></em><em><u>Question</u></em><em><u> </u></em><em><u>:</u></em><em><u>-</u></em><em><u> </u></em>

  • Sum of numbers = 90 .
  • Difference of numbers = 18 .

<em><u>Let </u></em><em><u>:</u></em><em><u>-</u></em><em><u> </u></em>

  • First Number be x .
  • Second number be y .

<em><u>According</u></em><em><u> to</u></em><em><u> </u></em><em><u>1</u></em><em><u>s</u></em><em><u>t</u></em><em><u> </u></em><em><u>condition</u></em><em><u> </u></em><em><u>:</u></em><em><u>-</u></em><em><u> </u></em>

: \implies x + y = 90

<u>According</u><u> to</u><u> </u><u>2</u><u>n</u><u>d</u><u> </u><u>condition</u><u> </u><u>:</u><u>-</u><u> </u>

: \implies x - y = 18

<em><u>Adding</u></em><em><u> the</u></em><em><u> </u></em><em><u>equations</u></em><em><u> </u></em><em><u>:</u></em><em><u>-</u></em><em><u> </u></em>

: \implies 2x = 18 + 90

: \implies 2x = 108

: \implies x = 54

<em><u>Therefore</u></em><em><u> </u></em><em><u>:</u></em><em><u>-</u></em><em><u> </u></em>

: \implies First number = 54

: \implies Second number = 36

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Step-by-step explanation: was uuu

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