Partial Differentiation
Notes
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See all →- What is a partial derivative of a function of two or three variables and what does it mean? In one line A partial derivative measures how a function of several variables changes when only one variable changes and all the others are... 1
- How do I differentiate a composite function z = f(x, y) when x and y depend on t? In one line If z=f(x,y) with x=x(t) and y=y(t) , then dz/dt=∂ z/∂ xdx/dt+∂ z/∂ ydy/dt : add the contributions of each path. Explained simply... 1
- What are higher-order and mixed partial derivatives, and why is u_xy usually equal to u_yx? In one line Differentiating a partial derivative again gives second-order derivatives u_xx,u_yy and the mixed ones u_xy,u_yx , which are equ... 1
- How do I use the chain rule when x and y depend on two new variables u and v? In one line If z=f(x,y) with x=x(u,v) , y=y(u,v) , then z_u=z_xx_u+z_yy_u and z_v=z_xx_v+z_yy_v ; every path from z to the new variable cont... 1
- How do I prove results like (∂/∂x + ∂/∂y + ∂/∂z)²u = −9/(x+y+z)² for a given function? In one line Compute the needed partial derivatives, combine them as the question asks, simplify using algebraic identities, and only then ap... 1
- What is a homogeneous function and how do I find its degree? In one line A function f(x,y) is homogeneous of degree n if scaling every variable by t scales the function by tⁿ : f(tx,ty)=tⁿf(x,y) . Expl... 1