i need help on calculus
derivative of integral (tanx, x^2) 1/(sqrt(2+x^4))
i think im supposed to use the first part of the fundamental law of calculus, but the only thing i can get from it is that the answer should be the function
so is the answer 1/(sqrt(2+x^4))
January 28, 2013
9 Comments • Newest first
take the natural log of the whole thing then differentiate lol
i'm not sure why people are suggesting integrals lol
[quote=AwakenedSoul]actually the question said derivative of the function, but the function had that squiggly thing and i dont know wats it called, so i call it integral[/quote]
It's exactly what I said and @above said also.
The problem is asking: take the DERIVATIVE of the INTEGRAL
The function in the Integral is f(x), right ---> and because it is an Integral, f(x) is the DERIVATIVE of a function ---> let's call that function F(x). So when you take the Anti-Derivative [integral] of f(x), you get F(x) ---> and then when you take the DERIVATIVE of that Integral ---> you get f(x) ---> which was the function in the Integral...you get it?
This is the FTC - Fundamental Theorem of Calculus.
[quote=AwakenedSoul]actually the question said derivative of the function, but the function had that squiggly thing and i dont know wats it called, so i call it integral[/quote]
The "squiggly thing" is called an integration symbol.
You're differentiating an integral, which leaves you with the original function without the integration symbol.
[quote=GreatRomantic]An integral is an anti-derivative. If you take the derivative of that integral. You just end up back where you started from.
"Take the DERIVATIVE of an INTEGRAL..." I think you know where this is headed now.[/quote]
actually the question said derivative of the function, but the function had that squiggly thing and i dont know wats it called, so i call it integral
By the Fundament Theorem of Calculus, The derivate of an indefinite integral is the function itself, so the answer is simply (tanx, x^2) 1/(sqrt(2+x^4))
Go to wolframalpha for any question about anything.
An integral is an anti-derivative. If you take the derivative of that integral. You just end up back where you started from.
"Take the DERIVATIVE of an INTEGRAL..." I think you know where this is headed now.
use substitution rule or w/e
http://mathmistakes.info/facts/CalculusFacts/learn/doi/doi.html
talks about derivative of an integral common mistakes. Might help you get an idea