# partial derivative of multivariable function

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 $\dfrac{\partial g}{\partial z}$?

• in two words: chain rule! :) – essay May 12 '14 at 13:35

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 $f(y) = 3y^2$).