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cj2222
- 14
- 0
can someone show me step by step how to find dy/dx of y=1/(x+y) using implicit differentiation?
Implicit differentiation is a mathematical technique used to find the derivative of an implicitly defined function, where the dependent variable is not isolated on one side of the equation. It is used when the function cannot be easily differentiated using traditional methods.
Implicit differentiation is used when the function is defined implicitly, meaning it is not in the form of y = f(x). It is also used when the function has both x and y variables and cannot be easily solved for y.
Explicit differentiation is used when the dependent variable is isolated on one side of the equation, while implicit differentiation is used when the dependent variable is not isolated. In explicit differentiation, the derivative is simply found by differentiating the function with respect to the independent variable. In implicit differentiation, the chain rule and product rule must also be applied.
The process for implicit differentiation involves taking the derivative of both sides of the equation with respect to the independent variable, using the chain rule and product rule as needed. The goal is to isolate the derivative of the dependent variable, dy/dx, on one side of the equation.
Implicit differentiation is important in science because it allows us to find the rate of change of a function when it is not explicitly defined. This can be useful in many applications, such as in physics, where functions may be defined implicitly and their derivatives can provide important information about the system being studied.