find the derivative of the function. f(x)=(u^2-9)/(u^2+9) from [2x,3x]

Question

zehanz · Answer

f is a function of x, but the formula has u in it...

anonymous · Answer

oh my bad i left out the du at the end. f(x)=(u^2-9)/(u^2+9)du

zehanz · Answer

Shouldn't there also be an integral sign in there somewhere?

abb0t · Answer

Do you mean find the anti-derivative?

anonymous · Answer

yeah theres an integral sign sorry

zehanz · Answer

So$$f(x)=\int\limits_{2x}^{3x}\frac{ u^2-9 }{ u^2+9 }du$$And you need f'(x), right?

anonymous · Answer

correct

zehanz · Answer

Using the Fundamental Theorem of Calculus:

$$f(x)=G(3x)-G(2x)$$where G is the antiderivative of the integrand.
The integrand being$$g(u)=\frac{ u^2-9 }{ u^2+9 }$$

Now all you have to do is:$$f'(x)=\left( G(3x)-G(2x) \right)'=...$$

zehanz · Answer

This turns into:$$f'(x)=(G(3x))'-(G(2x))'=3\cdot g(3x)-2 \cdot g(2x)=...$$So just plug in u=3x and u=2x in g(u) to get f'(x).