question ..

[al-horia]

Hi
I hope I did not bother you
I know I asked 3 questions till now
I really feel Embarrassment

my question is :

differentiate the given function

g(t)=((t^2)+([FONT=MathJax_Main]√t))/2t+5

we use the Quotient Rule
g(t)=((t^2)+(t^(1/2))/2t+5
g'(t)= ( ((2t+5)*(2t+(1/2)t^(-1/2)) - ((t^2+t^(1/2)*(2)) ) / (2t+5)^2
g'(t) =( (4t^2) + t^(1/2) + 10t + (5/2) * t^(-1/2) - 2t^2 - 2t ^ (1/2) ) / (2t+5)^2
g'(t) =( 2t^2 + 10t - t^(1/2) + (5/2) t ^ (-1/2 ) ) / [/FONT][FONT=MathJax_Main](2t+5)^2

the final answer must be equal
g'(t) = ( 4 ([/FONT][FONT=MathJax_Main]√t^5) + 20 ([/FONT][FONT=MathJax_Main]√t^3) - 2t + 5 ) / [/FONT][FONT=MathJax_Main](2t+5)^2[/FONT]

 

[tkhunny]

Embarrassment for what? If it was always easy, would we call it "learning"?

Check your notation a little. Taht denominator is not written as intended. (2t+5) would have been correct. The parentheses make quite a difference.

Your first step looks fine. I didn't check your algebra after that.

 

[mmm4444bot]

Hi
I hope I did not bother you
I know I asked 3 questions till now
I really feel Embarrassment

There is no need for embarrassment. You are properly following our posting guidelines, so you may feel free to start multiple threads.

my question is :

differentiate the given function

g(t)=((t^2)+([FONT=MathJax_Main]√t))/[/FONT][FONT=MathJax_Main]([/FONT][FONT=MathJax_Main]2t+5[/FONT][FONT=MathJax_Main])[/FONT][FONT=MathJax_Main]

we use the Quotient Rule

g(t)=((t^2)+(t^(1/2))/[/FONT][FONT=MathJax_Main]([/FONT][FONT=MathJax_Main]2t+5[/FONT][FONT=MathJax_Main])[/FONT][FONT=MathJax_Main]

g'(t)= ( [/FONT][FONT=MathJax_Main]([/FONT][FONT=MathJax_Main](2t+5)*(2t+(1/2)t^(-1/2)) - [/FONT][FONT=MathJax_Main]([/FONT][FONT=MathJax_Main](t^2+t^(1/2)*(2)) ) / (2t+5)^2

Your grouping symbols are wrong, in the line above.

You have 11 open parentheses, but you have only 9 closing parentheses

[/FONT]

[FONT=MathJax_Main]You may find it easier to use both ( ) and [ ], to avoid confusion.[/FONT]

[FONT=MathJax_Main]g'(t) =( 2t^2 + 10t - t^(1/2) + (5/2) t ^ (-1/2 ) ) / [/FONT][FONT=MathJax_Main](2t+5)^2[/FONT]

This result looks correct, to me.

Their answer rationalized the denominator in 1/sqrt(t), I think, but I can't verify their result.

I'm thinking that their answer is not correct as posted. Please check your typing on their answer.

Your answer is correct.

 

[mmm4444bot]

the final answer must be equal

g'(t) = ( 4 (√t^5) + 20 (√t^3) - 2t + 5 ) / (2t+5)^2

Okay -- I found their error. They left off a factor of 2sqrt(t) in the denominator.

It should be read:

g'(t) = [4√t^5 + 20√t^3 - 2t + 5] / [2√t (2t+5)^2]

 

[al-horia]

Okay -- I found their error. They left off a factor of 2sqrt(t) in the denominator.

It should be read:

g'(t) = [4√t^5 + 20√t^3 - 2t + 5] / [2√t (2t+5)^2]

dear
you are right
I did not right the final answer correct here

my question is how can I get this final answer correct

this is my work

g(t)=((t^2)+([FONT=MathJax_Main]√t))/2t+5[/FONT]
[FONT=MathJax_Main]
we use the Quotient Rule
g(t)=((t^2)+(t^(1/2))/2t+5
g'(t)= ( ((2t+5)*(2t+(1/2)t^(-1/2)) - ((t^2+t^(1/2)*(2)) ) / (2t+5)^2
g'(t) =( (4t^2) + t^(1/2) + 10t + (5/2) * t^(-1/2) - 2t^2 - 2t ^ (1/2) ) / (2t+5)^2
g'(t) =( 2t^2 + 10t - t^(1/2) + (5/2) t ^ (-1/2 ) ) / (2t+5)^2 this is my final answer

the final answer must be equal
g'(t) = ( 4 (√t^5) + 20 (√t^3) - 2t + 5 ) / (2t+5)^2 this is the final answer from book

as you see my final answer is difference to the book answer

can you tell me where is my error in my work?

thank you very much for your help [/FONT]

 

[mmm4444bot]

[FONT=MathJax_Main]g'(t) =( 2t^2 + 10t - t^(1/2) + (5/2) t ^ (-1/2 ) ) / (2t+5)^2 this is my final answer

the final answer must be equal
g'(t) = ( 4 (√t^5) + 20 (√t^3) - 2t + 5 ) / (2t+5)^2 this is the final answer from book

as you see my final answer is difference to the book answer

can you tell me where is my error in my work?

[/FONT]

Perhaps, you do not understand my English?

In my previous reply, I told you that the book's answer is NOT correct.

The book's answer is missing the factor shown in red below.

[FONT=MathJax_Main]g'(t) = ( 4 (√t^5) + 20 (√t^3) - 2t + 5 ) / [/FONT][FONT=MathJax_Main][(2[/FONT]√[FONT=MathJax_Main]t)[/FONT][FONT=MathJax_Main](2t+5)^2[/FONT][FONT=MathJax_Main]]



[/FONT]:arrow: :arrow: :arrow: :arrow: Your answer is correct:

[FONT=MathJax_Main]g'(t) =( 2t^2 + 10t - t^(1/2) + (5/2) t ^ (-1/2 ) ) / (2t+5)^2
[/FONT]


If you would like to convert your answer (above) to the corrected book's form (shown above in blue & red), then multiply your answer by (2[FONT=MathJax_Main]√t[/FONT])/(2[FONT=MathJax_Main]√t[/FONT]). :cool: