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miguel hernandez
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First of all thanks for the help, i have a problem finding a good explanation of de ecuation (d/dx)f=(∂f/∂x)+(∂f/∂y)*(dy/dx) could anyone write me a good explanation of this ecuation? thanks for the help
Implicit differentiation is a mathematical concept used to find the derivative of an equation that is not explicitly expressed in terms of a dependent variable. It is commonly used when an equation cannot be easily solved for the dependent variable, and involves differentiating both sides of the equation with respect to the independent variable.
Implicit differentiation is used when an equation is not in the form of y = f(x), meaning the dependent variable is not explicitly expressed in terms of the independent variable. It is commonly used in multivariable calculus, differential equations, and physics problems.
The process of implicit differentiation involves differentiating both sides of an equation with respect to the independent variable, treating the dependent variable as a function of the independent variable. This will result in an equation with the derivative of the dependent variable in terms of the derivative of the independent variable.
Explicit differentiation involves finding the derivative of an equation explicitly expressed in terms of the independent variable, while implicit differentiation involves finding the derivative of an equation that is not explicitly expressed in terms of the dependent variable. In other words, implicit differentiation is used for equations that cannot be easily solved for the dependent variable.
Some real-world applications of implicit differentiation include optimization problems in economics and physics, determining the rate of change in a chemical reaction, and finding the velocity and acceleration of a moving object in physics.