1. ## differentiation problems

I am in my first calculus class and I am completely lost. The teacher is very intelligent, but her teaching style is not very effective for me. I have always made great grades in math courses, but I have been doing poorly in this course. My book is Technical Calculus by Peter Kuhfittig and I have a difficult time learning the information from the book. I have a couple of easy problems that I can't figure out how to answer. I was hoping that somebody might be able to answer them and break down the process for me. I have a test on Thursday and I would like to find a free online resource to learn this information. I apologize for asking you to answer questions for me, but I really have no option since I must turn in my homework (graded for correctness) and I don't have a clue how to answer the questions. I will try to help others on this forum when I can.

2. Originally Posted by patrickg
I am in my first calculus class and I am completely lost. The teacher is very intelligent, but her teaching style is not very effective for me. I have always made great grades in math courses, but I have been doing poorly in this course. My book is Technical Calculus by Peter Kuhfittig and I have a difficult time learning the information from the book. I have a couple of easy problems that I can't figure out how to answer. I was hoping that somebody might be able to answer them and break down the process for me. I have a test on Thursday and I would like to find a free online resource to learn this information. I apologize for asking you to answer questions for me, but I really have no option since I must turn in my homework (graded for correctness) and I don't have a clue how to answer the questions. I will try to help others on this forum when I can.

#32 $\displaystyle y = \sqrt{ln(x)} dx$

First, change this to:

$\displaystyle y = (ln(x))^{\frac{1}{2}}$

Then you will need to use the chain rule. Which I assume you have learned?

Let $\displaystyle f(x) = x^{\frac{1}{2}}$
Let $\displaystyle g(x) = ln(x)$

So,
$\displaystyle f'( x) = \frac{1}{2}x^{-\frac{1}{2}}$
$\displaystyle g'(x) = \frac{1}{x}$

Chain rule = $\displaystyle f'(g(x)) \cdot g'(x)$

$\displaystyle y' = \frac{\frac{1}{2} (ln(x))^{-\frac{1}{2}}}{x}$

$\displaystyle = \frac{1}{2x\sqrt{lnx}}$

#44. $\displaystyle r_1 = \frac{r_2}{ln(r_2)}$

You will need to use the quotient rule:

Let
$\displaystyle f(x) = r_2$
$\displaystyle g(x) = ln(r_2)$

$\displaystyle f'(x) = 1$
$\displaystyle g'(x) = \frac{1}{r_2}$

Quotient rule: $\displaystyle \frac{fg' - f'g}{g^2}$

Can you try to solve it?

#38 $\displaystyle y = x^x$

You will need to use the natural log to solve this. Start by taking the natural log of both sides:

$\displaystyle ln(y) = ln(x)^x$

$\displaystyle ln(y) = x ln(x)$

Now differentiate with respect to x, using chain rule on the right and product rule on the left:

$\displaystyle \frac{1}{y}y' = x(\frac{1}{x}) + ln(x)$

Then just solve for y'

#40 $\displaystyle y = (sin(x))^x$

This one will use both the chain rule and implicit differentiation like we did in the last one. See if you can try it.
Good luck!

3. I am going to start going over it and I will post back after a while. Thank you very much for getting me started down the right track.