Scalar Derivative and Partial Derivatives
Derivative
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
Find a Derivative
Example:
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
Scalar derivative rules
Partial Derivatives
A partial derivative of a function of several variables is its derivative with respect to one of those variables, with the others held constant.
'The partial derivative with respect to x' is written as or where is called 'del' or 'curly dee'.
Find Partial Derivatives
Consider a function with two variables (x and y):
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
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