Differentiate, but do not simplify: f(x)=cos(x)/x

Thread starter ttpp1124
Start date May 12, 2020
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Differentiate Simplify

In summary, differentiating a function means finding its derivative, which is important for understanding its behavior and making predictions. Differentiation is different from simplification, as it focuses on understanding the function rather than simplifying it. The derivative of f(x)=cos(x)/x is -sin(x)/x - cos(x)/x^2, and it is possible to differentiate a function without simplifying it, although the resulting derivative may be complex.

May 12, 2020

ttpp1124

Homework Statement: can someone check to see if my work is correct?

Relevant Equations: n/a

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May 12, 2020

etotheipi

Yes, but make your minuses ##-## and dots ##\cdot## clearer. They look the same in your answer.

May 12, 2020

member 587159

I think it is time to learn Latex, don't you agree?

May 12, 2020

robphy

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1. What does it mean to differentiate a function?

Differentiation is a mathematical process that involves finding the rate of change of a function. It is essentially finding the slope of the function at a given point, which can help determine the behavior of the function and its relationship with other variables.

2. How do you differentiate a function?

To differentiate a function, you must use the rules of differentiation, such as the power rule, product rule, and chain rule. These rules involve taking the derivative of each term in the function and combining them to find the overall derivative.

3. Why is it important to differentiate a function?

Differentiation is important because it allows us to understand the behavior of a function and how it changes with respect to its variables. This information is useful in many fields, including physics, economics, and engineering.

4. What does it mean to not simplify a function?

Not simplifying a function means leaving it in its original form without reducing or combining any terms. In the case of the given function, f(x)=cos(x)/x, not simplifying means leaving it as it is without combining the cosine and x terms.

5. Why should we differentiate, but not simplify, the function f(x)=cos(x)/x?

Differentiating the function f(x)=cos(x)/x allows us to find the derivative, which provides information about the behavior of the function. Not simplifying the function allows us to see the original form and understand the relationship between the cosine and x terms. This can be useful in certain applications or when solving more complex problems.