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Debaa
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How do I figure whether to do implicit differentiation or just explicit?? Thanks for the answer.
You really need to do a bit more research before posting questions such as this. You already received one warning today for a substandard post, so I won't hit you with another for this post.Debaa said:How do I figure whether to do implicit differentiation or just explicit??
Implicit differentiation is used to find the derivative of a function that is not explicitly defined in terms of the independent variable. It is often used when the dependent variable cannot be easily isolated and solved for. On the other hand, explicit differentiation is used to find the derivative of a function that is explicitly defined in terms of the independent variable.
Implicit differentiation is typically used when the function involves both the dependent and independent variables and cannot be easily solved for the dependent variable. It is also useful when finding the derivative of an equation that is not in the standard form of y = f(x).
To perform implicit differentiation, you will need to use the chain rule and the product rule. First, differentiate each term in the equation with respect to the independent variable. Then, solve for the derivative of the dependent variable by moving all terms with the dependent variable to one side and factoring it out.
Yes, implicit differentiation can be used for all types of functions, including polynomial, exponential, trigonometric, and logarithmic functions. However, it is most commonly used for functions involving multiple variables or when the dependent variable cannot be easily isolated.
Implicit differentiation has limitations when it comes to finding higher-order derivatives. It can become increasingly complex and time-consuming as the number of variables and terms in the function increases. In these cases, it may be more efficient to use explicit differentiation or other methods such as logarithmic differentiation.