Question

Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function.

Answer 1

u = 1/x

Answer 2

let \[
f'(t) = \arctan t
\]Then \[
\int_7^uf'(t)\;dt = f(u) - f(7)
\]

Answer 3

\[
\frac{d}{du}\left[f(u)-f(7)\right] = f'(u) = \arctan u
\]Remember that \(f'(7) =\frac d{du} \arctan 7 = 0\)

Answer 4

That is the FTC part.

Answer 5

The other part is simply: \[
\frac{du}{dx} = \frac{d}{dx}u = \frac{d}{dx}\left(\frac 1x\right)
\]

Answer 6

what should I put in these two space

Answer 7

Actually, I shouldn't have written \(f'(7)\), that is notation failure. It should remain as \(\frac{d}{du}f(7)\).

Answer 8

If you understand what I said, you know what to do.