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anonymous
 5 years ago
find dx/dy for y^2 = 5x+2
anonymous
 5 years ago
find dx/dy for y^2 = 5x+2

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Have you heard of implicit differentiation?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yes i was wondering what the answer was as my teacher provided no answers. just wanted to double check =]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Well, anyway, you need to take the derivative with respect to x on both sides. The lefthand side, being a function of x (i.e. y = y(x) will be differentiated using the chain rule). \[y^2=5x+2 \rightarrow \frac{d}{dx}y^2=\frac{d}{dx}(5x+2) \rightarrow2yy'=5\]\[y'=\frac{5}{2y} \rightarrow y'=\frac{5}{2\sqrt{5x+2}}, \frac{5}{2\sqrt{5x+2}}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0what is the difference between dx/dy and dy/dx?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0dy/dx is the rate of change in y with respect to x, and dx/dy is the rate of change of x with respect to y. In the first instance, we're measuring the change in y as a function of x (i.e. *we* change x and the function moves because of it). In the second, we're measuring the change in x as a function of y (i.e. *we* change y and x is forced to move because of it).

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Does that make sense?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yes that does thank you very much! so for the question you just helped me out with you had found dx/dy right ?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0or did you find dy/dx?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0No...what you're technically doing is called an 'operation' in mathematics. You can move from one statement to another in mathematics and perform operations at each step, the only catch is that if you perform an operation on one side of an equation, you need to perform the operation on the other side.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0So, we needed the derivative of this equation with respect to x. I said we needed to take the derivative with respect to x on both sides.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0When we did it to the righthand side, it was easy, since\[\frac{d}{dx}(5x+2)=5\]...you're used to that.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0But when we did it to the lefthand side, it wasn't so obvious as to what we were doing. What we're doing in implicit differentiation is using the chain rule. So, on the lefthand side,

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[\frac{d}{dx}y^2=\frac{dy^2}{dy}.\frac{dy}{dx}=2y \frac{dy}{dx}=2yy'\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Do you see how we've used the chain rule? Nothing dodgy happened.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0awwww i see. hahahas i'm really stupid at maths. Well THANK YOU SO SO MUCH for your time and patience in explaining! =D

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0np ;) and I'm pretty sure you're not stupid!

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0You should be able to do your other problem now.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0THANK YOU THANK YOU !
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