Step Expression Explanation
1 ∂/∂x (x/y) Start with the original function
2 = 1/y ∂/∂x(x) Treat y as a constant while differentiating with respect to x
3 = 1/y × 1 Differentiate x to get 1
4 = 1/y Multiply by the constant 1/y


example of finding a partial derivative

Step Expression Explanation
1 ∂/∂y (x/y) Start with the original function
2 = ∂/∂y (x × y⁻¹) Rewrite x/y as x × y⁻¹
3 = x ∂/∂y(y⁻¹) Treat x as a constant while differentiating with respect to y
4 = x × -1 × y⁻² Differentiate y⁻¹ to get -1 × y⁻²
5 = -x × y⁻² Simplify -1 × y⁻² to -y⁻²
6 = -x/y² Simplify -y⁻² to -1/y²
7 = -x/y² Multiply by the constant x
8 = -x/y² The partial derivative is -x/y²