Differentiation is a core concept in calculus that calculates the rate of change of a function.

The fundamental principles governing differentiation encompass rules such as the power rule, sum rule, difference rule, product rule, quotient rule, constant rule, and chain rule.

To differentiate a function with multiple terms, apply the sum/difference rule and then differentiate each term separately.

The chain rule, a method employed in differentiating composite functions, asserts that the derivative of such a function equals the product of the outer function's derivative with the derivative of the inner function.

To differentiate logarithmic functions, use the chain rule in conjunction with the derivative of the natural logarithm function.

The product rule in differentiation is a key method for finding the derivative of two functions multiplied together. It states that the derivative of the product of two functions equals the sum of the first function's derivative times the second function, add to the first function times the derivative of the second function.

The quotient rule is a technique used to differentiate the quotient of two functions. It states that the derivative of such a quotient equals the difference between difference between the product of the first function's derivative and the second function, and the product of the first function and the second function's derivative, all divided by the square of the second function.

To differentiate parametric functions, find the derivatives of the functions with respect to the parameter, and then use the chain rule to find the derivative of one function with respect to the other.

Some common applications of differentiation include finding maximum and minimum values of functions, determining rates of change, solving optimization problems, and analyzing the behavior of functions in various fields such as Physics, Engineering, Economics, and Biology.