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Term-by-term Differentiation

Definition

Term-by-term differentiation refers to the process of finding the derivative of each term in a series individually. It allows us to differentiate each term separately without affecting the other terms.

Analogy

Think of a group project where each member has their own task. Just like how each member works on their part independently, term-by-term differentiation allows us to differentiate each term in a series separately.

Related terms

Power Rule: The power rule is a formula used to find the derivative of a function that involves raising it to a power. It states that if we have a function f(x) = x^n, then its derivative is given by f'(x) = nx^(n-1).

Chain Rule: The chain rule is used when we have composite functions, which are functions within functions. It helps us find the derivative of these composite functions by breaking them down into simpler parts and applying the chain rule formula.

Product Rule: The product rule is used when we need to find the derivative of two or more functions multiplied together. It provides a formula for finding this derivative without having to expand and differentiate each term separately.