Scalar Derivative and Partial Derivatives
Last updated
Last updated
In calculus, derivative can be approached in two different ways. One is geometrical (as a slope of a curve) and the other one is physical (as a rate of change). The process of finding a derivative is called "differentiation"
'The derivative of' is commonly written as or
A partial derivative of a function of several variables is its derivative with respect to one of those variables, with the others held constant.
a) Partial derivative with respect to x (Treat y as a constant like a random number 12)
b) Partial derivative with respect to y (Treat x as a constant)
Link: - Matrix Calculus For Deep Learning - MathIsFun: Introduction to Derivatives - MathIsFun: Partial Derivatives - Khan Academy: Basic Derivative Rules
means the slope or "rate of change" at any point in the graph/function is 2x. So when x=2 the slope is 2x = 4
'The partial derivative with respect to x' is written as or where is called 'del' or 'curly dee'.
Consider a function with two variables (x and y):