Jaweria
I need help with 11 questions of Derivatives problems in Calculus 1. Can anyone help me with that please let me know, I will really appreciate it.
Delete
Share
This Question is Closed
Curry
Best Response
You've already chosen the best response.
0
just post, i got you.
Jaweria
Best Response
You've already chosen the best response.
0
ok first one is: (2x-3)^2+(4y-5)^2=10
Jaweria
Best Response
You've already chosen the best response.
0
and we need to find dy/dx for all of them.
binarymimic
Best Response
You've already chosen the best response.
1
you can either use implicit differentiation from the start, or you can begin by isolating the y variable.
Jaweria
Best Response
You've already chosen the best response.
0
second question is: x^2sin(x)+y^2cos(y)=1
binarymimic
Best Response
You've already chosen the best response.
1
likewise for the second
Jaweria
Best Response
You've already chosen the best response.
0
yeah we have to do implicit diffentiation but I am really stuck in all of them.
binarymimic
Best Response
You've already chosen the best response.
1
i'll get you started with (2x-3)^2+(4y-5)^2=10
Jaweria
Best Response
You've already chosen the best response.
0
ohh thank you so much
binarymimic
Best Response
You've already chosen the best response.
1
|dw:1359266294450:dw|
binarymimic
Best Response
You've already chosen the best response.
1
idk if you can read the edge of it, it should say = 0
Jaweria
Best Response
You've already chosen the best response.
0
yeah i can
Jaweria
Best Response
You've already chosen the best response.
0
but after the paranthesis is that a multiply by 2 or its a power of 2 for the first one
binarymimic
Best Response
You've already chosen the best response.
1
multiplication
Jaweria
Best Response
You've already chosen the best response.
0
ok
Jaweria
Best Response
You've already chosen the best response.
0
but then we have to simplify more right?
binarymimic
Best Response
You've already chosen the best response.
1
yeah you would have to isolate y'
Jaweria
Best Response
You've already chosen the best response.
0
ok can we go through this together till the end?
binarymimic
Best Response
You've already chosen the best response.
1
sure
Jaweria
Best Response
You've already chosen the best response.
0
thank u :)
binarymimic
Best Response
You've already chosen the best response.
1
|dw:1359266644304:dw|
binarymimic
Best Response
You've already chosen the best response.
1
|dw:1359266753423:dw|
Jaweria
Best Response
You've already chosen the best response.
0
how did u get -2?
binarymimic
Best Response
You've already chosen the best response.
1
oh my bad, that should be a 12
binarymimic
Best Response
You've already chosen the best response.
1
|dw:1359266876031:dw|
Jaweria
Best Response
You've already chosen the best response.
0
oh ok
binarymimic
Best Response
You've already chosen the best response.
1
|dw:1359266992506:dw|
Jaweria
Best Response
You've already chosen the best response.
0
and do we have to put y^1 before paranthesis?
binarymimic
Best Response
You've already chosen the best response.
1
where?
Jaweria
Best Response
You've already chosen the best response.
0
its ok I got it
binarymimic
Best Response
You've already chosen the best response.
1
ok. try the second one whenever you are comfortable
Jaweria
Best Response
You've already chosen the best response.
0
ok
Jaweria
Best Response
You've already chosen the best response.
0
ok I have a feeling that I ll again get stuck with this one:
Jaweria
Best Response
You've already chosen the best response.
0
x^2sin(x)+y^2cos(y)=1
binarymimic
Best Response
You've already chosen the best response.
1
just think of differentiating y like you were differentiating any other variable (except x). remember to write the "dy/dx" or " y' " after you differentiate
Jaweria
Best Response
You've already chosen the best response.
0
ok
binarymimic
Best Response
You've already chosen the best response.
1
like here's an example:
if i differentiate y*sin y with respect to x:
= y cos(y) * y' + sin(y) * y'
= y' [y cos(y) + sin(y)]
binarymimic
Best Response
You've already chosen the best response.
1
it's the same as if you were differentiating 'u', as in
differentiate: sin(x^2)
let u = x^2 and differentiate sin(u)
d/dx sin(u) = cos(u) * du = cos(x^2) * du
Another way of saying that is: cos(x^2) * u'
The only difference here is, we can write du in terms of x very easily. With implicit differentiation, we normally can't do that, but it's the same concept.
Jaweria
Best Response
You've already chosen the best response.
0
hmmm if you dont mind can we go over this problem because my brain is not working at all with all of these i am sorry but thats the truth all my 11 questions are due tomorrow online :(
Jaweria
Best Response
You've already chosen the best response.
0
I m still learning
binarymimic
Best Response
You've already chosen the best response.
1
x^2sin(x)+y^2cos(y)=1
let's start with the easy part. if we're going to differentiate both sides, the right side becomes 0. what does x^2 sin(x) become ?
Jaweria
Best Response
You've already chosen the best response.
0
2x cos(x)
binarymimic
Best Response
You've already chosen the best response.
1
are you sure?
Jaweria
Best Response
You've already chosen the best response.
0
not much
binarymimic
Best Response
You've already chosen the best response.
1
don't forget the product rule
Jaweria
Best Response
You've already chosen the best response.
0
i always mess up on product rule and chain rule
binarymimic
Best Response
You've already chosen the best response.
1
\[\frac{ d }{ dx } x^{2} \sin x = x^{2} \cos x + \sin x * 2x\]
binarymimic
Best Response
You've already chosen the best response.
1
"first times the derivative of the second, plus second times the derivative of the first"
Jaweria
Best Response
You've already chosen the best response.
0
ohh ok
binarymimic
Best Response
You've already chosen the best response.
1
now try differentiating y^2cos(y)
Jaweria
Best Response
You've already chosen the best response.
0
ok
Jaweria
Best Response
You've already chosen the best response.
0
not sure if I did it right or not
Jaweria
Best Response
You've already chosen the best response.
0
|dw:1359268366069:dw|
binarymimic
Best Response
You've already chosen the best response.
1
the left part is almost right, just need the negative sign (the derivative of cos is -sin
the other part would become:
cos(y) * 2y * dy/dx
Jaweria
Best Response
You've already chosen the best response.
0
oh ok
binarymimic
Best Response
You've already chosen the best response.
1
so i think you got that right, too, just needed the dy/dx ?
Jaweria
Best Response
You've already chosen the best response.
0
yes
binarymimic
Best Response
You've already chosen the best response.
1
\[x^{2} \cos x + 2x \sin x + \frac{ dy }{ dx } * -y^{2} \sin y + \frac{ dy }{ dx } * 2y \cos y\]
Jaweria
Best Response
You've already chosen the best response.
0
so that will be |dw:1359268690019:dw|
binarymimic
Best Response
You've already chosen the best response.
1
|dw:1359268763927:dw|
Jaweria
Best Response
You've already chosen the best response.
0
ok
binarymimic
Best Response
You've already chosen the best response.
1
you need to isolate dy/dx now
Jaweria
Best Response
You've already chosen the best response.
0
yeah ok
Jaweria
Best Response
You've already chosen the best response.
0
|dw:1359269043320:dw|
Jaweria
Best Response
You've already chosen the best response.
0
is that right?
binarymimic
Best Response
You've already chosen the best response.
1
yep perfect
you can eliminate the minus sign on the outside if you wanted to by swapping the terms in the denominator to make it:
y^2 sin y - 2y cos y
but thats just a matter of preference
Jaweria
Best Response
You've already chosen the best response.
0
ok thanks
binarymimic
Best Response
You've already chosen the best response.
1
wait let me double check something
Jaweria
Best Response
You've already chosen the best response.
0
couple more please if you dont mind?
Jaweria
Best Response
You've already chosen the best response.
0
ok
binarymimic
Best Response
You've already chosen the best response.
1
ok. sorry. if you had more questions you might want to start a new post
Jaweria
Best Response
You've already chosen the best response.
0
oh ok
binarymimic
Best Response
You've already chosen the best response.
1
after a few of these, implicit differentiation will be easy for you
Jaweria
Best Response
You've already chosen the best response.
0
this is the first time ever I am using this site can you suggest me that how to start new post?
Jaweria
Best Response
You've already chosen the best response.
0
Yeah I am trying my best.