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 $z=(1x^2\cos y)^\frac{1}{3}$.
Last edited by skipjack; April 2nd, 2019 at 02:27 PM. 

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derivative, partial 
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