This article tells about when derivative, partial derivatives and gradients are used and differences between them.
1. Derivative:
Derivatives are used when the function has only one variable.
example: f(x) = 5x , f(z) = sin(z)+3
In the above examples x, z are variables. Since each function is a function of single variable, derivative can be applied.
Function is differentiated with respect to a variable.
2. Partial Derivative:
Partial derivatives are used when the function has two or more variables.
Partial derivative is taken with respect to(w.r.t) one variable, while other variables are considered as constants.
example: f(x,y,z) = 2x+3y+4z , where x,y,z are variables. Partial derivative can be taken w.r.t each variable.
Derivative is represented by ‘d’, where as partial derivative is represented by ‘∂’
3. Gradient:
Gradient is a differential operator applied to functions which has two or more variables.
Gradient yields a vector whose components are partial derivatives of the function with respect to its variables.
Gradient packs together all partial derivatives into a vector.
Let us consider same example f(x,y,z) = 2x+3y+4z.
Let vector θ = [x, y, z].
Gradient is denoted by del operator ∇(f(θ))
