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Jaweria
 2 years ago
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.
Jaweria
 2 years ago
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.

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Jaweria
 2 years ago
Best ResponseYou've already chosen the best response.0ok first one is: (2x3)^2+(4y5)^2=10

Jaweria
 2 years ago
Best ResponseYou've already chosen the best response.0and we need to find dy/dx for all of them.

binarymimic
 2 years ago
Best ResponseYou've already chosen the best response.1you can either use implicit differentiation from the start, or you can begin by isolating the y variable.

Jaweria
 2 years ago
Best ResponseYou've already chosen the best response.0second question is: x^2sin(x)+y^2cos(y)=1

binarymimic
 2 years ago
Best ResponseYou've already chosen the best response.1likewise for the second

Jaweria
 2 years ago
Best ResponseYou've already chosen the best response.0yeah we have to do implicit diffentiation but I am really stuck in all of them.

binarymimic
 2 years ago
Best ResponseYou've already chosen the best response.1i'll get you started with (2x3)^2+(4y5)^2=10

binarymimic
 2 years ago
Best ResponseYou've already chosen the best response.1dw:1359266294450:dw

binarymimic
 2 years ago
Best ResponseYou've already chosen the best response.1idk if you can read the edge of it, it should say = 0

Jaweria
 2 years ago
Best ResponseYou've already chosen the best response.0but after the paranthesis is that a multiply by 2 or its a power of 2 for the first one

Jaweria
 2 years ago
Best ResponseYou've already chosen the best response.0but then we have to simplify more right?

binarymimic
 2 years ago
Best ResponseYou've already chosen the best response.1yeah you would have to isolate y'

Jaweria
 2 years ago
Best ResponseYou've already chosen the best response.0ok can we go through this together till the end?

binarymimic
 2 years ago
Best ResponseYou've already chosen the best response.1dw:1359266644304:dw

binarymimic
 2 years ago
Best ResponseYou've already chosen the best response.1dw:1359266753423:dw

binarymimic
 2 years ago
Best ResponseYou've already chosen the best response.1oh my bad, that should be a 12

binarymimic
 2 years ago
Best ResponseYou've already chosen the best response.1dw:1359266876031:dw

binarymimic
 2 years ago
Best ResponseYou've already chosen the best response.1dw:1359266992506:dw

Jaweria
 2 years ago
Best ResponseYou've already chosen the best response.0and do we have to put y^1 before paranthesis?

binarymimic
 2 years ago
Best ResponseYou've already chosen the best response.1ok. try the second one whenever you are comfortable

Jaweria
 2 years ago
Best ResponseYou've already chosen the best response.0ok I have a feeling that I ll again get stuck with this one:

binarymimic
 2 years ago
Best ResponseYou've already chosen the best response.1just think of differentiating y like you were differentiating any other variable (except x). remember to write the "dy/dx" or " y' " after you differentiate

binarymimic
 2 years ago
Best ResponseYou've already chosen the best response.1like 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
 2 years ago
Best ResponseYou've already chosen the best response.1it'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
 2 years ago
Best ResponseYou've already chosen the best response.0hmmm 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 :(

binarymimic
 2 years ago
Best ResponseYou've already chosen the best response.1x^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 ?

binarymimic
 2 years ago
Best ResponseYou've already chosen the best response.1don't forget the product rule

Jaweria
 2 years ago
Best ResponseYou've already chosen the best response.0i always mess up on product rule and chain rule

binarymimic
 2 years ago
Best ResponseYou've already chosen the best response.1\[\frac{ d }{ dx } x^{2} \sin x = x^{2} \cos x + \sin x * 2x\]

binarymimic
 2 years ago
Best ResponseYou've already chosen the best response.1"first times the derivative of the second, plus second times the derivative of the first"

binarymimic
 2 years ago
Best ResponseYou've already chosen the best response.1now try differentiating y^2cos(y)

Jaweria
 2 years ago
Best ResponseYou've already chosen the best response.0not sure if I did it right or not

binarymimic
 2 years ago
Best ResponseYou've already chosen the best response.1the 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

binarymimic
 2 years ago
Best ResponseYou've already chosen the best response.1so i think you got that right, too, just needed the dy/dx ?

binarymimic
 2 years ago
Best ResponseYou'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
 2 years ago
Best ResponseYou've already chosen the best response.0so that will be dw:1359268690019:dw

binarymimic
 2 years ago
Best ResponseYou've already chosen the best response.1dw:1359268763927:dw

binarymimic
 2 years ago
Best ResponseYou've already chosen the best response.1you need to isolate dy/dx now

binarymimic
 2 years ago
Best ResponseYou've already chosen the best response.1yep 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

binarymimic
 2 years ago
Best ResponseYou've already chosen the best response.1wait let me double check something

Jaweria
 2 years ago
Best ResponseYou've already chosen the best response.0couple more please if you dont mind?

binarymimic
 2 years ago
Best ResponseYou've already chosen the best response.1ok. sorry. if you had more questions you might want to start a new post

binarymimic
 2 years ago
Best ResponseYou've already chosen the best response.1after a few of these, implicit differentiation will be easy for you

Jaweria
 2 years ago
Best ResponseYou've already chosen the best response.0this is the first time ever I am using this site can you suggest me that how to start new post?

Jaweria
 2 years ago
Best ResponseYou've already chosen the best response.0Yeah I am trying my best.
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