What is the difference between Derivative and Differential?

Hint: The concept of derivative functions distinguishes calculus from other branches of mathematics. Differential is a subfield of calculus that refers to infinitesimal difference in some varying quantity and is one of the two fundamental divisions of calculus. The other branch is called integral calculus.

Complete step-by-step answer:
Differential : Differential is one of the fundamental divisions of calculus, along with integral calculus. It is a subfield of calculus that deals with infinitesimal change in varying quantities.
Differentiation is a method of computing a derivative which is the rate of change of the output y of the function with respect to the change of the variable x.
Differential equations are equations that contain unknown functions and some of their derivatives.
Derivative: The concept of derivative of a function is one of the most powerful concepts in mathematics. The derivative of a function is usually a new function which is called the derivative function or the rate function.
The derivative of a function represents an instantaneous rate of change in the value of a dependent variable with respect to the change in value of the independent variable. It’s a fundamental tool of calculus which can also be interpreted as the slope of the tangent line. It measures how steep the graph of a function is at some given point on the graph.

Note: The rate of change of one variable with respect to another variable is called a derivative and the equations which express the relationship between these variables and their derivatives are called differential equations.