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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.
 one year ago
 one year 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.
 one year ago
 one year ago

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

JaweriaBest ResponseYou've already chosen the best response.0
and we need to find dy/dx for all of them.
 one year ago

binarymimicBest ResponseYou'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.
 one year ago

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

binarymimicBest ResponseYou've already chosen the best response.1
likewise for the second
 one year ago

JaweriaBest ResponseYou've already chosen the best response.0
yeah we have to do implicit diffentiation but I am really stuck in all of them.
 one year ago

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

binarymimicBest ResponseYou've already chosen the best response.1
dw:1359266294450:dw
 one year ago

binarymimicBest ResponseYou've already chosen the best response.1
idk if you can read the edge of it, it should say = 0
 one year ago

JaweriaBest ResponseYou'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
 one year ago

JaweriaBest ResponseYou've already chosen the best response.0
but then we have to simplify more right?
 one year ago

binarymimicBest ResponseYou've already chosen the best response.1
yeah you would have to isolate y'
 one year ago

JaweriaBest ResponseYou've already chosen the best response.0
ok can we go through this together till the end?
 one year ago

binarymimicBest ResponseYou've already chosen the best response.1
dw:1359266644304:dw
 one year ago

binarymimicBest ResponseYou've already chosen the best response.1
dw:1359266753423:dw
 one year ago

binarymimicBest ResponseYou've already chosen the best response.1
oh my bad, that should be a 12
 one year ago

binarymimicBest ResponseYou've already chosen the best response.1
dw:1359266876031:dw
 one year ago

binarymimicBest ResponseYou've already chosen the best response.1
dw:1359266992506:dw
 one year ago

JaweriaBest ResponseYou've already chosen the best response.0
and do we have to put y^1 before paranthesis?
 one year ago

binarymimicBest ResponseYou've already chosen the best response.1
ok. try the second one whenever you are comfortable
 one year ago

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

binarymimicBest ResponseYou'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
 one year ago

binarymimicBest ResponseYou'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)]
 one year ago

binarymimicBest ResponseYou'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.
 one year ago

JaweriaBest ResponseYou'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 :(
 one year ago

binarymimicBest ResponseYou'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 ?
 one year ago

binarymimicBest ResponseYou've already chosen the best response.1
don't forget the product rule
 one year ago

JaweriaBest ResponseYou've already chosen the best response.0
i always mess up on product rule and chain rule
 one year ago

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

binarymimicBest ResponseYou've already chosen the best response.1
"first times the derivative of the second, plus second times the derivative of the first"
 one year ago

binarymimicBest ResponseYou've already chosen the best response.1
now try differentiating y^2cos(y)
 one year ago

JaweriaBest ResponseYou've already chosen the best response.0
not sure if I did it right or not
 one year ago

binarymimicBest ResponseYou'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
 one year ago

binarymimicBest ResponseYou've already chosen the best response.1
so i think you got that right, too, just needed the dy/dx ?
 one year ago

binarymimicBest ResponseYou've already chosen the best response.1
\[x^{2} \cos x + 2x \sin x + \frac{ dy }{ dx } * y^{2} \sin y + \frac{ dy }{ dx } * 2y \cos y\]
 one year ago

JaweriaBest ResponseYou've already chosen the best response.0
so that will be dw:1359268690019:dw
 one year ago

binarymimicBest ResponseYou've already chosen the best response.1
dw:1359268763927:dw
 one year ago

binarymimicBest ResponseYou've already chosen the best response.1
you need to isolate dy/dx now
 one year ago

binarymimicBest ResponseYou'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
 one year ago

binarymimicBest ResponseYou've already chosen the best response.1
wait let me double check something
 one year ago

JaweriaBest ResponseYou've already chosen the best response.0
couple more please if you dont mind?
 one year ago

binarymimicBest ResponseYou've already chosen the best response.1
ok. sorry. if you had more questions you might want to start a new post
 one year ago

binarymimicBest ResponseYou've already chosen the best response.1
after a few of these, implicit differentiation will be easy for you
 one year ago

JaweriaBest ResponseYou'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?
 one year ago

JaweriaBest ResponseYou've already chosen the best response.0
Yeah I am trying my best.
 one year ago
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