I need help with this question Please Urgently!! Find dy/dx: x^2-xy+y^3=1.
Please anyoneeee I really need a help
okay so you will take the derivative of each thing like... 2x-y+x(dy/dx)+3y^2(dy/dx)=0 get the dy.dx on one side
x(dy/dx)+3y^2(dy/dx)=y-2x factor dy/dx
dy/dx(x+3y^2)=y-2x
dy/dx= (y-2x)/(x+3y^2)
Good c: I see one minor boo boo though,\[\huge \frac{d}{dx}(-xy)=-y\color{orangered}{-}x\frac{dy}{dx}\] @cherio12
ohh where is it?
ya good call
forgot to distribute the negative
but where I cant see that which one?
The fancy math not showing up for you pinky? :O The derivative of the second term, the -xy. It should produce 2 negative terms.
the denominator should be 3y^2-x
opps lolz sorry thanks i am blind :P
Sorry one more question if anyone can help pleaseeeeee
\[xe ^{2y}=5x+y ^{2}\]
you want the derivative,correct?
the 1st degree partials
No not partials :) This is Calc 1. Implicit Differentiation.
or is this a differential equation?
yes I want derivative its an implicit differentiation
Taking the derivative of the left side, here is the setup for product rule,\[\large \left(xe^{2y}\right)'=(x)'e^{2y}+x(e^{2y})'\]
hmm ok
Really? Already confused? :( Hmm you should have learned product rule at this point <:o hmmm
^^^ lol take it easy
no no not confuse lolz sorry
I m following you
What sweet...?
differentiate both sides with respect to x. The left side requires the product rule, and so do the two terms on the right side.
Here's the left side\[\frac{ \delta }{ \delta x }xe^{2y} = e^{2y}+2x(\frac{ dy }{ dx })e^{2y}\]
ok
The process is the same for the right hand side. As you can see, we had to implicitly differentiate with respect to x, since we couldn't explicitly differentiate with respect to x, since y, being a function of x, is unknown.
ok
I understand, I skipped pre-calc and trig and went straight to calc 1. I didn't fully understand most of the material until calc 2 lol
ohh :(
I m really upset thought its due tomorrow :(
hey hey, you just have to clear your mind, relax, and look at the material anew, ignoring all frustration and anxiety.
Do you want me to explain what implicit differentiation is?
yes please and if you can also help me to solve this whole problem I will appreciate your help :(
well the answer to this problem is:\[\frac{ \delta }{ \delta x}xe^{2y} = \frac{ \delta }{ \delta x}(5x +y^2)=\frac{ \delta }{ \delta x}(5x) + \frac{ \delta }{ \delta x}(y^2)\]\[e^{2y}+2x \frac{ \delta y }{ \delta x } e^{2y} = 5 + 2y(\frac{ \delta y }{ \delta x })\] isolate dy/dx:\[2x \frac{ \delta y }{ \delta x } e^{2y} - 2y(\frac{ \delta y }{ \delta x }) = 5 - e^{2y}\]\[\frac{ \delta y }{ \delta x } (2xe^{2y} - 2y) = 5 - e^{2y}\]\[\frac{ \delta y }{ \delta x } = \frac{ 5 - e^{2y} }{ (2xe^{2y} - 2y) }\]
seems complicated, but it really isn't. Math notation makes everything more difficult. I'm using delta x instead of dx because y might be a function of other variables besides x
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