- #1
ttpp1124
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- Homework Statement
- can someone see if my work is right?
- Relevant Equations
- n/a
Differentiate, but do not simplify ##f(x)=5^{tan(\sqrt{ x})}##
- Thread starter ttpp1124
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- Differentiate Simplify
In summary, the conversation discusses the importance of being able to check one's own work in STEM fields, as it is ultimately their responsibility to ensure the accuracy of their calculations. This skill is crucial in real world scenarios where there may not be anyone else to double check their work.
- #2
BvU
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You can do it yourself -- PF isn't for stamp-approving homework 
https://www.wolframalpha.com/input/?i=(5^tan(sqrt(x)))'
(Or is that cheating ?)
Whatever, we see you master ##\LaTeX## quite well !
https://www.wolframalpha.com/input/?i=(5^tan(sqrt(x)))'
(Or is that cheating ?)
Whatever, we see you master ##\LaTeX## quite well !
- #3
DaveE
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If you continue in the STEM fields, you will find yourself with a job where you are responsible for doing correct calculations on your own. Out in the real world people don't check your work because either they don't know how (you're the expert), or they have their own work to do. The ultimate check is the bridge collapses (or not), or the patient dies (or not), or you have a really happy (or pissed off) customer.
An important skill to develop is the ability to check your own work. Step one is do the calculation, step two is convince yourself that you did it right (because we all make mistakes).
An important skill to develop is the ability to check your own work. Step one is do the calculation, step two is convince yourself that you did it right (because we all make mistakes).
1. What does it mean to "differentiate" a function?
Differentiation is a mathematical process that calculates the rate of change of a function with respect to its independent variable. In simpler terms, it is a way to find the slope of a curve at any given point.
2. Why is it important to differentiate a function?
Differentiation is important because it allows us to analyze the behavior of a function and make predictions about its values. It is also a fundamental tool in calculus and is used in various real-world applications such as physics, engineering, and economics.
3. What does it mean to "simplify" a function?
Simplifying a function means to manipulate it algebraically in order to make it easier to understand or work with. This can involve combining like terms, factoring, or rewriting the function in a more compact form.
4. Why should the function "##f(x)=5^{tan(\sqrt{ x})}##" not be simplified?
In some cases, simplifying a function can change its behavior and make it more difficult to analyze. In the case of "##f(x)=5^{tan(\sqrt{ x})}##", simplifying it would involve using logarithms, which can alter the shape of the function and make it harder to differentiate.
5. How do you differentiate "##f(x)=5^{tan(\sqrt{ x})}##"?
To differentiate "##f(x)=5^{tan(\sqrt{ x})}##", we can use the chain rule, which states that the derivative of a composite function is equal to the derivative of the outer function multiplied by the derivative of the inner function. In this case, the derivative is: "##f'(x)=5^{tan(\sqrt{ x})} \cdot sec^2(\sqrt{ x}) \cdot \frac{1}{2\sqrt{ x}}##".
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