IMPLICIT DIFFERENTIATION Meaning and
Definition
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Implicit differentiation is a calculus technique used to find the derivative of an equation that is implicitly defined. It is employed when a given equation cannot be easily solved for one variable in terms of the other variables.
Implicit differentiation involves differentiation with respect to a specific variable while treating the other variables as implicit functions of that variable. By considering these implicit functions and applying the chain rule, implicit differentiation allows for the determination of the derivatives of both dependent and independent variables.
The process begins by identifying the variables involved in the equation and differentiating each term with respect to the desired variable. The derivative of any variable that is not being differentiated is treated as an implicit derivative, resulting in a coefficient multiplied by the derivative of the variable. Afterward, the equation is rearranged to isolate the derivative of the desired variable.
Implicit differentiation is particularly useful when differentiating functions that cannot be readily manipulated to solve for the desired variable, where explicit differentiation would be challenging or impossible. It allows for the calculation of derivatives even when equations are given in the form of implicit relationships between variables. Implicit differentiation is a powerful tool in calculus, enabling the determination of the slope of curves and the rates of change related to these relationships.
Common Misspellings for IMPLICIT DIFFERENTIATION
- umplicit differentiation
- jmplicit differentiation
- kmplicit differentiation
- omplicit differentiation
- 9mplicit differentiation
- 8mplicit differentiation
- inplicit differentiation
- ikplicit differentiation
- ijplicit differentiation
- imolicit differentiation
- imllicit differentiation
- im0licit differentiation
- impkicit differentiation
- imppicit differentiation
- impoicit differentiation
- implucit differentiation
- impljcit differentiation
- implkcit differentiation
- implocit differentiation
- impl9cit differentiation
Etymology of IMPLICIT DIFFERENTIATION
The word "implicit differentiation" has its etymology rooted in Latin and Greek.
The term "implicit" comes from the Latin word "implicitus", which means "entwined" or "combined". It is derived from the Latin verb "implicare", which means "to involve" or "to entwine".
The word "differentiation" has its origins in the Greek word "διαφορά" (diaphorá), meaning "difference" or "distinction". It is derived from the Greek verb "διαφέρω" (diaphérō), which means "to differ" or "to distinguish".
Thus, when combined, "implicit differentiation" refers to the mathematical concept of differentiating an equation implicitly, where the derivative of an equation involving multiple variables is determined, without explicitly solving for any specific variable.
