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y = x ln x
[tex]\frac{dy}{dx} = \frac{1}{x ln x} \cdot 1[/tex]
Is that correct?
[tex]\frac{dy}{dx} = \frac{1}{x ln x} \cdot 1[/tex]
Is that correct?
I was taught that way. How did you get 1/x?SphericalStrife said:Hmm I'm not great at this but,
y = x lnx
I was gunna say.. that whenever you take the derivative of logs.. 1/function * derivative of that function
so that'd give you
y = (1/xlnx)(1/x)
How do you know it?SphericalStrife said:1/x is the known derivative of lnx
The product rule is a formula used in calculus to find the derivative of two functions that are multiplied together. It states that the derivative of the product of two functions is equal to the first function times the derivative of the second function, plus the second function times the derivative of the first function.
The product rule should be applied when you have a function that can be broken down into two or more functions multiplied together. It is used to find the derivative of the overall function.
To use the product rule, you first need to identify the two functions that are being multiplied together. Then, you apply the formula by taking the derivative of each function and multiplying it by the other function, and then adding those two terms together.
Yes, the product rule can be extended to more than two functions. For example, if you have three functions multiplied together, you would take the derivative of each function and multiply it by the other two functions, and then add all three terms together.
The product rule is important in calculus because it allows us to find the derivative of a product of two or more functions. This is a crucial concept in calculus, as it is used in many applications such as optimization, related rates, and curve sketching.