Question

help me on derivative problem. I'll upload the problem below.

Answer 1

So first lets rewrite the formula for T as a constant times L:
\[T = 2\pi \sqrt{\frac{L}{g}} \Rightarrow T = \frac{2\pi}{\sqrt{g}}*\sqrt{L}\]
Now we can take the derivative with respect to L :
\[T = \frac{2\pi}{\sqrt{g}}*\sqrt{L} \Rightarrow T' = \frac{2\pi}{\sqrt{g}}*\frac{1}{2\sqrt{L}}\]

Answer 2

so the answer is pretty much when you simply 2π/sqrt(LG)

Answer 3

the two's will cancel out, but yes thats the general form.

Answer 4

\[\frac{dT}{dL} = \frac{\pi}{\sqrt{gL}}\]