Without computing integral, how to compute first derivative

You want to use the derivative form of the fundamental theorem of calculus to compute the derivative of the integral. :)
 
raymond said:
sorry，just a typo
f’(x)=arctan(x)+x/(x^2+1)-arctan(x)?
Click to expand...
What theorem did you use to derive that? - Write it explicitly.

Why do have "?" in there? Why do you doubt your answer?

Remember to write "arctan" in functional notation as "arctan(x)". Those parentheses are important indicators.
 
Subhotosh Khan said:
What theorem did you use to derive that? - Write it explicitly.

Why do have "?" in there? Why do you doubt your answer?

Remember to write "arctan" in functional notation as "arctan(x)". Those parentheses are important indicators.
Click to expand...
Indeed，the question ask me to answer the first derivative of the function without compute the integral, so I write it out by the fundamental calculus theorem and ask whether my answer is true or not, the ?just a question mark
 
Subhotosh Khan said:
What theorem did you use to derive that? - Write it explicitly.

Why do have "?" in there? Why do you doubt your answer?

Remember to write "arctan" in functional notation as "arctan(x)". Those parentheses are important indicators.
Click to expand...
For the brackets, I know it is important, but I skip it in here since lazy
 
raymond said:
Indeed，the question ask me to answer the first derivative of the function without compute the integral, so I write it out by the fundamental calculus theorem and ask whether my answer is true or not, the ?just a question mark
Click to expand...
Your answer for [f'(x)] is correct. Why do you doubt your answer?
 
To raymond above you wrote \(\displaystyle f(x)\) for function notation. You did not write \(\displaystyle f\,x\).
But \(\displaystyle \arctan\) is also a function yet you write \(\displaystyle \arctan\,t\) when it should be \(\displaystyle \arctan(t)\).
 
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