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Suppose that $f(x,y,z,w)=0=g(x,y,z,w)$ determine $z$ and $w$ as differentiable functions of $x$ and $y$ . I need to find out $\dfrac{\partial z}{\partial x}$ at $y$ .

I tried to approach using total differential form but got stuck. Please provide some insight.

Please do say whether total differential form can be used or not.

The Learner
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  • The answer is in the form of partial derivative only – The Learner Sep 29 '19 at 14:01
  • Someone please edit the question, I am not able to give the partial derivative sign – The Learner Sep 29 '19 at 14:05
  • The partial derivative sign $\partial$ is simply \partial – glowstonetrees Sep 29 '19 at 14:06
  • Sorry for inconvenience, please provide some initial step or approach so that I can do this problem – The Learner Sep 29 '19 at 14:09
  • You can use this page for future reference. It covers all the basics in the main post, and you can also find some of the more advanced stuff if you scroll down to the other posts. https://math.meta.stackexchange.com/questions/5020/mathjax-basic-tutorial-and-quick-reference – glowstonetrees Sep 29 '19 at 14:10
  • Implicit differentiation of the equations $f=0$ and $g=0$ with respect to $x$ will give you a $2 \times 2$ linear system to solve for $\partial z/\partial x$ and $\partial w/\partial x$. – Hans Lundmark Sep 29 '19 at 17:03

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