LOGARITHMIC DIFFERENTIATION Meaning and
Definition
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Logarithmic differentiation is a method used in calculus to differentiate functions that are expressed as a product, quotient, or power of other functions. It involves taking the logarithm of both sides of an equation, then differentiating implicitly, and finally solving for the derivative of the original function.
This method is particularly useful when a function is difficult to differentiate using regular differentiation techniques such as the product or quotient rule. By taking the logarithm of the function, it can be simplified into a form that is easier to differentiate. This is done by using the properties of logarithms to manipulate the equation and simplify expressions.
Logarithmic differentiation can also be applied when a function is raised to a power, as it allows for simplification and differentiation of complicated expressions. By taking the logarithm of both sides, the power rule can be used to differentiate, and the final result can then be obtained by undoing the logarithm.
Overall, logarithmic differentiation is a technique that can be employed to differentiate functions that are not easily differentiable by regular methods. By utilizing logarithms, it allows for simplification and application of known differentiation rules, enabling the determination of the derivative of the original function.
Etymology of LOGARITHMIC DIFFERENTIATION
The word "logarithmic differentiation" is composed of two main components: "logarithmic" and "differentiation".
The term "logarithmic" has its roots in the Greek word "logos", meaning "word" or "ratio", and "arithmos", meaning "number". It was introduced in the early 17th century by the Scottish mathematician John Napier, who invented logarithms. Logarithms are mathematical tools used to simplify computations involving exponents and have various applications in different branches of science and engineering.
The term "differentiation" comes from the Latin word "differentiatus", which is the past participle of "differentiare", meaning "to differ" or "to distinguish between". In mathematics, differentiation is a fundamental operation used to compute the rate at which a function changes as its inputs change. It helps find slopes, rates of change, and other crucial information about functions.
