Having problems with these 3 questions

N

Norse man

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Apr 4, 2011
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Can anyone help and solve these problems please and show me how you got to the final answer?


Q1. Find the value of the derivative of Y = xtan²(2x – 1) at = 4 + ?
8

Q2. Find the accurate to 4 decimal places, the value of the derivative of y = sin(x²+2)
1nx
at x = e (‘e’ is the base of the natural logarithms and can be taken as 2.718282 accurate to seven significant figures)



Q3. If I = ? 2x____ dx
x²+6x +8 and when x = -1, I = 4(1n3 – 1n5), find the value of I when x = 1
 
Q3. If I = ? 2x____ dx
x²+6x +8 and when x = -1, I = 4(1n3 – 1n5), find the value of I when x = 1
Click to expand...

What is this?.

Do you mean?:

\(\displaystyle I=\int\frac{2x}{x^{2}+6x+8}dx\)

When x=-1, then \(\displaystyle I=4(ln(3)-ln(5))\),

find the value of I when x=1.
 
Norse man said:
Can anyone help and solve these problems please and show me how you got to the final answer?


Q1. Find the value of the derivative of Y = xtan²(2x – 1) at = 4 + ?
8

Find Y' first - then evaluate at the given point.

Q2. Find the accurate to 4 decimal places, the value of the derivative of y = sin(x²+2)
1nx
at x = e (‘e’ is the base of the natural logarithms and can be taken as 2.718282 accurate to seven significant figures)

Find y' first - then evaluate at the given point.

Please share your work with us, indicating exactly where you are stuck - so that we may know where to begin to help you.



Q3. If I = ? 2x____ dx
x²+6x +8 and when x = -1, I = 4(1n3 – 1n5), find the value of I when x = 1
Click to expand...
 
Yes that is the equation for Q3 I need help in answering.


For the other two questions I need help with


Also I have just realised in Q1 where it states = 4 + ? it should have a 8 underneath it (divide by 8)


Also I have just realised in Q2 where it states sin(x²+2) should have 1nx underneath it (divide by 1nx)
 
Yes that equation you have put is correct for Q3. can you show me how to work it out starting from the top so to speak to the final answer.

Also I have just noticed in Q1 where it states = 4 + ? it should have an 8 underneath it (divide by 8)


Also I have just noticed in Q2 where it states sin(x²+2) it should 1nx underneath it (divide by 1nx)


So if you can help solve the other two questions I would really appreciate it!
 
What have you done about those problems - on your own?

Do you know how to find derivatives of a function?

Do you know how to use chain rule and product rule of derivatives?
 
Hi Subhotosh,

I have not done anything on my own yet apart from read a text book and confuse myself even more. I would like to be shown how to solve the 3 questions from to start to finish, so I can learn. I find it easier that way.

many thanks
 
Can you tell me - why are you doing these advanced problems?

for #1

You need to know first derivative of tan(x)

You need to know then derivative of tan(2x-1)

You need to know then derivative of tan[sup:1xbw3h3l]2[/sup:1xbw3h3l](2x-1)

You need to know then derivative of x * tan[sup:1xbw3h3l]2[/sup:1xbw3h3l](2x-1)

Then evaluate above result at x = 1/2 + ?/8

How many of the steps mentioned above can you complete?

We will go from there......
 
I am doing a distance learning course and I have some questions to answer. I have managed to answer some but these 3 questions I can not get my head round
 
Can you follow the steps that I had outlined above?
 
No thats why I would like to go through each of the 3 questions step by step to find and understand the answer
 
If you do not know the derivative of tan(x) - then this class is way over your limit.
 
I think your right but I still need to answer the questions. In the past a fully worked out question has helped me understand. Sometimes reading a book does not help me.

Also I am not getting much help from the course, hence why I am trying to use this site
 
Norse,

Your best bet is to do some less complex exercises of the items Subhotosh listed (review derivatives, then derivatives using the chain rule, then derivatives using the product rule, then derivatives of trig functions.) Sometimes you've got to go backwards to move forwards and the more I learn about math, the more true that is...

-good luck
Brandon
 
If I understand your problem correctly, perhaps the best way to tackle #3 is to use partial fractions and rewrite it as:

\(\displaystyle \int\frac{2x}{x^{2}+6x+8}dx=4\int\frac{1}{x+4}dx-2\int\frac{1}{x+2}dx\)

This leads to \(\displaystyle 4ln|x+4|-2ln|x+2|+C\)

When x=-1, we get:

\(\displaystyle 4ln(3)+C\)

Thus, C must equal \(\displaystyle -4ln(5)\)

\(\displaystyle 4ln(x+4)-2ln(x+2)-4ln(5)\)

When x=1, then \(\displaystyle I=-2ln(3)\)
 
Hi Galactus,

Thanks so much for looking and showing me how its done. For that particular question it gave you the 4 answers below to choose from. So would B be the closest to the solution?

a 501n3

b 1n9

c 101n1/3

d 1n1/9
 
I am not understanding what you have written. Is that first one supposed to be 50ln(3).

Is that 1 meant to be an l ?. That is a lowercase L, not a 1. As in LN for Natural Logarithm.

You poor thing. You are starting off behind the 8 ball. :wink:

Anyway, \(\displaystyle ln(1/9)=-2ln(3)\).

This is the same. Just in another form due to the laws of logs.

\(\displaystyle -2ln(3)=ln(3^{-2})=ln(1/9)\)
 
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