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 April 2nd, 2019, 08:16 AM #1 Math Team     Joined: Jul 2013 From: काठमाडौं, नेपाल Posts: 901 Thanks: 61 Math Focus: सामान्य गणित Partial derivative Find $\displaystyle \frac{\partial z}{\partial x}$ for $\displaystyle x^{2}+\cos y +z^{3}=1$ Please explain what it means.
 April 2nd, 2019, 10:34 AM #2 Senior Member   Joined: Dec 2015 From: somewhere Posts: 605 Thanks: 88 Two ways to find it. (1) Just find the partial derivative to both sides of equality. (2) Write z explicitly and find the partial derivative. Also $\displaystyle \partial z =(\partial z / \partial x )\cdot dx+(\partial z / \partial y )\cdot dy$. Last edited by skipjack; April 2nd, 2019 at 02:26 PM.
 April 2nd, 2019, 12:55 PM #3 Global Moderator   Joined: May 2007 Posts: 6,807 Thanks: 717 Start with $z=(1-x^2-\cos y)^\frac{1}{3}$. Thanks from topsquark Last edited by skipjack; April 2nd, 2019 at 02:27 PM.

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