Differenciate twice or integrate twice?

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In summary, the conversation discusses differentiating the function f(x) = (ln x)^2 and determining its second derivative, or f''(x). The individual asking the question is unsure if they need to differentiate or integrate twice, and the other person explains that it means differentiating twice. They also mention using the chain rule to actually perform the differentiation, with an example of applying it to the given function.
  • #1
jinx007
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I am confuse a question state f(x) = (ln x )^2 ... i skip a part..

show that f'' (x) = 0 (not concern with the answer but what does f'' means is it that i have to differenciate twice or integrate twice..??)

my second question: how to differenciate y = (ln x )^2
 
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  • #2


It means differentiate twice.

To actually do it, think about using the chain rule...
 
  • #3


danago said:
It means differentiate twice.

To actually do it, think about using the chain rule...


chain rule that is dy/dx = dy/dt x dt/dx of course i must apply it
 
  • #4


Yes, and with y = (ln x )^2 , t= ln x so you want (d(t^2)/dt)(d ln(x)dx)
 

1. What is the difference between differentiating twice and integrating twice?

Differentiating twice refers to taking the derivative of a function twice, while integrating twice means finding the indefinite integral of a function twice. In other words, differentiating twice reduces the order of the function by two, while integrating twice increases the order of the function by two.

2. When should I differentiate twice and when should I integrate twice?

Differentiating twice is useful for finding the slope or rate of change of a function, while integrating twice is useful for finding the area under a curve or the total value of a function. It ultimately depends on the specific problem you are trying to solve.

3. Can you differentiate or integrate a function an infinite number of times?

Technically, yes. However, in most cases, differentiating or integrating a function more than a few times will either result in a constant function or an undefined function.

4. Is it possible to differentiate or integrate a constant function?

Yes, but the result will always be 0. This is because the derivative of a constant is 0, and the integral of 0 is a constant.

5. Can I use the chain rule or the product rule when differentiating or integrating twice?

Yes, the chain rule and product rule can be applied when differentiating or integrating twice. However, it may be more complex and require multiple steps to solve the problem.

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