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Let $f: \mathbb{R}^3 \to \mathbb{R}^3$ be a differentiable function, and define $g: \mathbb{R}^2 \to \mathbb{R}^3$ by $g(y,z) = f(1,y,z)$. Then how can one find $\dfrac{\partial g}{\partial y}$ and $\dfrac{\partial g}{\partial z}$?

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    $\begingroup$ in two words: chain rule! :) $\endgroup$ – essay May 12 '14 at 13:35
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Treat everything except the variable of integration as constants. For example, to find $\dfrac{\partial g}{\partial y}$, ignore everything and differentiate with respect to y (the same way you would differentiate a function like $f(y) = 3y^2$).

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