Free module · Calculus & mathematical models
Multivariable Calculus & Partial Derivatives
Change one input, follow several inputs together, and measure interactions.
partial derivatives · gradients · Hessians · constraints
The building blocks
- A function can accept two inputs.
- Change one input while keeping the other fixed.
- Take one partial derivative
- Combine sensitivities along a path
- Use gradients, Hessians and constraints
Lessons in this module
- Start with two inputs: change only one
- Partial derivatives: holding the other inputs fixed
- Gradients, directional derivatives and Jacobians
- Hessians, mixed derivatives and second-order scenarios
- Constrained optimisation and multiple integrals
Practice and apply
- Separate a partial from a total change — f(x,y)=x²y+3y² at (2,1). The path has dx/dt=3, dy/dt=−1.
- Two-input value — For f(x,y)=x+2y, find f(2,4).
Work through the practice exercises · Quant development tools