Guys I was just wanting to know if someone could give me some more implicit differentiation problems to work on. I have solved all of the ones in my textbook and the ones on the first 10 pages of Google. I was thinking that someone could either invent some or pull a couple from another text. I will post the answers when I get them done tonight. Also I am looking for some with trig or natural log particularly where there is some distribution involved. Just some, but not all of them have to be this way. As always I thank you for you help!

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here are some from my text (do they look familiar? the text is widely used, it might be the same as yours), i'll see if i can get others

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No this is Great! I have never seen these before. I will post the answers in an hour or so. Thanks Jhevon.

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here are some more. sorry that some of the questions are blurry, the text is huge and so i can't get it to scan very well (i tried several times). you can see some though

whoops, that's way to small.

i'll try to repost in pieces so its larger

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here are some. for 18 and 20, find dy/dx

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more

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ok, those should keep you off the streets for a while

I have the first 13 problems worked out. I solve each of these twice to be sure that I had the correct answer (this is what I do when I am taking tests):




















I am still working on the others!!

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I think you did very well, not completely correct on all of them however. here is my analysis:

for questions 1-4, you got all the (b)'s and (c)'s incorrect, but judging by your performance in part (a), i'm sure it was becuase you misread the questions.

Incorrect:
you got two and a half questions incorrect. what's with the half? allow me to explain.

for question 8, you had the wrong answer. why is it wrong? hint: c is a constant

for 10 part (a), you had 5x^4 in the bottom, when you should have 5y^4. this is just an honest mistake i think, since you got the right answer in part (b) (which was really the same thing as part (a) according to how you did it). this is the half incorrect i was talking about.

question 12 is also wrong. recheck your work to see if you can spot the error

Rewrite:
the following are not questions you got wrong. you were correct, however, there were more efficient ways to write your answers, try to identify what i did to go from your answers to "better" answers.

3(a)

Your answer: y' = x^-2/-y^-2

Better answer: y' = - y^2/x^2

4(a)

Your answer: y' = (-1/2)x^(-1/2)/(1/2)y^(-1/2)

Better answer: y' = - y^(1/2)/x^(1/2) = - sqrt(y)/sqrt(x)

5

Your answer: y' = -2x/2y

Better answer: y' = -x/y

6

Your answer: y' = -2x/-2y

Better answer: y' = x/y

13

Your answer: y' = 4sin(x)sin(y)/4cos(x)cos(y)

Better answer: y' = tan(x)tan(y)

for 1-4, i wouldn't really worry about part (c), part (a) and (b) have the stuff you need to be practicing

Jhevon I worked #12 out again. What did I do wrong I mean I distributed out the cos(xy^2)? What do you spot as the problem? Let me know as I am coming closer and closer to mastering this technique...

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this answer is correct. the first time you did it you had cos(xy^2)2y in the bottom, you left out the x. recheck your work to see why this happened, so you dont make the same mistake again

Jhevon I worked #8 out again. This time I treated "c" as a constant. I remember my teacher telling me about this in class when I asked him about it. Why not write a 1 or a 2 instead of a "c". Either way it goes to zero. Here is an update of problem 8:

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that is correct. and what your professor said is correct. just remember, the derivative of any constant is zero, if the way you remember that is to put a 1 or 2 for some constant c, then so be it

good job qbkr21! do you see why you got the (b) parts wrong in questions 1-4?

We are not in the month of October, this was a trick. I see what they wanted me to do. In these problem there wasn't more than one y' in the problem, and you were also given y=. The case of Explicit. You could:


1. Solve for Y
2. Then differentiate the question

In step b it says use "Explicit" which means you are given what the value of y= is equal do. In this case I would just compute the derivative using the properties and rules I know.

Whereas "Implicit" means you are not given y=. You are just given some equation and asked to find y'.

P.S. I can already sense where all of this is leading to in Calc 2 which as I already stated I am taking this summer. We are going to go backwards. Given y' and y'' and even y''' what is y=?. This my friend is integration and that is why I am already trying to learn the rules and procedures of computing it now so I am not lost later on....

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