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jgens
Gold Member
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Could someone please explain to me how implicit differentiation is an application of the chain rule? It would be much appreciated. By the way, if it helps, I'm a junior in high school. Thanks.
Implicit differentiation is a mathematical technique used to find the derivative of an equation that is not explicitly written in terms of one variable. It is commonly used when the equation contains both the dependent and independent variables, making it difficult to solve for the derivative using traditional methods.
Explicit differentiation involves finding the derivative of a function that is explicitly written in terms of one variable. In contrast, implicit differentiation involves finding the derivative of a function that is not explicitly written in terms of one variable.
Implicit differentiation is commonly used when the equation contains both the dependent and independent variables, making it difficult to solve for the derivative using traditional methods. It is also used when the equation is not easily solvable for the derivative using other techniques.
The steps for performing implicit differentiation are as follows:
Implicit differentiation has various applications in physics, engineering, and economics. It is often used to find the rate of change in a system, such as the speed of an object moving along a curved path or the rate of change in a production function. It is also useful in optimization problems, where the goal is to maximize or minimize a certain quantity.