Engineering Math Practice Test: Partial Differentiation — Flashcards

Partial Differentiation topics include: Limits and derivatives of variables, implicit and partial differentiation, eulers theorem, jacobians, quadrature, integral sign differentiation, total derivative, implicit partial differentiation and functional dependence.

Partial differentiation is a mathematical process that finds the derivative of a function with respect to one of its variables, while holding the other variables constant. It's used in vector calculus and differential geometry.

Partial differentiation is more general than ordinary differentiation, which finds the derivative with respect to only one variable. 

To partially differentiate a multivariable function with respect to one variable, you can:
Consider all other variables constant
Take the derivative normally 

For example, if f is a function of x and y, you can assume y is constant to take the derivative of f with respect to x. 

The symbol ∂ indicates a partial derivative. For example, u = u(x,t) means differentiate u(x,t) with respect to t, treating x as a constant. 

Partial differentiation is used when you take one of the tangent lines of the graph of a function and obtain its slope. The partial derivative is a way to find the slope in either the x or y direction, at the point indicated. 

Related Test: Engineering Math Practice Test: Differential Calculus