Question

Need help with applied calculus 1

Answer 1

I got this for the derivative of f with respect to L,
\[\frac{ -1 }{ L^2 }*(\frac{ T }{ P })^\frac{ 1 }{ 2 }+\frac{ 1 }{ 4L }(\frac{ T }{ P })^{\frac{ -1 }{ 2 }}\]

Answer 2

im not confident this is right

Answer 3

doesn't look too good.

\[f = \dfrac{1}{2L} \sqrt{\dfrac{T}{\rho}}\]

keeping T and rho constant means that you are essentially looking at \(\dfrac{d}{dL} (C \; L^{-1})\). where C is constant \(= \dfrac{1}{2} \sqrt{\dfrac{T}{\rho}}\)

Answer 4

oh i see, let me do it on paper first and ill tell you what i get

Answer 5

or if you prefer \(\large C \dfrac{d}{dL} ( \; L^{-1})\) or \(\large C \dfrac{d}{dL} ( \; \frac{1}{L})\)

Answer 6

is this right?