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 Differential Equations Ordinary and Partial Differential Equations Math Forum

 September 1st, 2016, 05:23 AM #1 Newbie   Joined: Sep 2016 From: York Posts: 2 Thanks: 0 Quick differentiation problem Hi, I'm Josh, just had a problem I've been thinking about and I think I'm missing a piece of... so... It's a bit of implicit differentiation, I just need to know how to implicitly differentiate half of an equation. Which is sqrt(x+y), differentiating with respect to x. obviously ( sqrt of x ) prime is 1/2(x)^-.5, I just was confused about the chain rule-- does it come into play at all here? With the y? And so... thanks. September 1st, 2016, 07:12 AM #2 Senior Member   Joined: Sep 2015 From: USA Posts: 2,529 Thanks: 1389 $\dfrac {d}{dx} (x+y) = 1$ $\dfrac {d}{dy} (x+y) = 1$ so in both cases the factor caused by the application of the chain rule is simply 1. September 1st, 2016, 11:26 AM #3 Newbie   Joined: Sep 2016 From: York Posts: 2 Thanks: 0 I want to know why though. Like what happens to the dy? Is it just not there at all? September 1st, 2016, 11:33 AM #4 Senior Member   Joined: Dec 2013 From: some subspace Posts: 212 Thanks: 72 Math Focus: real analysis, vector analysis, numerical analysis, discrete mathematics If we have $\displaystyle y = y(x)$ and we have some function, say $\displaystyle x^2 + y^2 = 9$ (a circle), then the implicit derivative of this with respect to $\displaystyle x$ is: $\displaystyle 2x + 2yy' = 0$. $\displaystyle 2x$ is the derivative of $\displaystyle x^2$ $\displaystyle 2yy'$ is the derivative of $\displaystyle y^2 = y(x)^2$ by using the chain rule. $\displaystyle 0$ is the derivative of $\displaystyle 9$. A warning, though, implicit differentiation can be dangerous if you don't know whether or not the $\displaystyle y$ really is a function. Thanks from topsquark Tags differentiation, problem, quick Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post MathMathHelloMath Algebra 3 January 7th, 2011 11:42 PM qynn Elementary Math 2 December 6th, 2010 03:22 PM Hobstweedl Algebra 1 September 14th, 2007 06:00 AM gruffyddd Calculus 3 September 11th, 2007 06:47 AM MathMathHelloMath Calculus 3 December 31st, 1969 04:00 PM

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