Changes

If

If

:<math>f(x,y,z) = \frac{x \sin{x} y^2}{z}\,</math>

:<math>f(x,y,z) = \frac{x y^2 \sin{x}}{z}\,</math>

we have

we have

:<math>\frac{\partial}{\partial x} f(x,y,z) = \frac{y^2 (x \cos{x} + \sin{x})}{z}</math>

:<math>\frac{\partial}{\partial x} f(x,y,z) = \frac{y^2 (x \cos{x} + \sin{x})}{z}</math>

:<math>\frac{\partial}{\partial y} f(x,y,z) = \frac{2 y x \sin{x}}{z}</math>

:<math>\frac{\partial}{\partial y} f(x,y,z) = \frac{2 x y \sin{x}}{z}</math>

:<math>\frac{\partial}{\partial z} f(x,y,z) = \frac{- x y^2 \sin{x}}{z^2}</math>

:<math>\frac{\partial}{\partial z} f(x,y,z) = \frac{- x y^2 \sin{x}}{z^2}</math>

Here are some alternative notations for partial derivatives:

Here are some alternative notations for partial derivatives: