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Physics345
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Moved from a technical forum
- Homework Statement
- Question: FIND ##\frac{\partial z}{\partial x}, \frac{\partial z}{\partial t}##
Given
##z= x^{y}##
##x =\sqrt{s+t}##
##y=ts^{2}##
- Relevant Equations
- ##\frac{\partial z}{\partial t} =\frac{\partial z}{\partial x}\frac{\partial x}{\partial t}+\frac{\partial z}{\partial y}\frac{\partial y}{\partial t}##
Solution:
##\frac{\partial z}{\partial x} = yx^{y -1}+1##
##\frac{\partial z}{\partial t} =\frac{\partial z}{\partial x}\frac{\partial x}{\partial t}+\frac{\partial z}{\partial y}\frac{\partial y}{\partial t}##
##\frac{\partial z}{\partial t} = (\frac{yx^{y-1} + 1}{2\sqrt{s+t}}) + x^{y}\ln{(y)}s^{2}##
This is my first time doing the chain rule and my professor doesn't give us the answers for questions. So I'm here to ask you guys if I did this correct. I'm very confused was I supposed to input the values given after completion or not?
Thanks
##\frac{\partial z}{\partial x} = yx^{y -1}+1##
##\frac{\partial z}{\partial t} =\frac{\partial z}{\partial x}\frac{\partial x}{\partial t}+\frac{\partial z}{\partial y}\frac{\partial y}{\partial t}##
##\frac{\partial z}{\partial t} = (\frac{yx^{y-1} + 1}{2\sqrt{s+t}}) + x^{y}\ln{(y)}s^{2}##
This is my first time doing the chain rule and my professor doesn't give us the answers for questions. So I'm here to ask you guys if I did this correct. I'm very confused was I supposed to input the values given after completion or not?
Thanks
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