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## Main Question or Discussion Point

Could anyone give a hand in solving this problem?

In shallow ocean water, the frequency of the wave action (number of wave crests passing a given point per second) is given by f= [(g/(2PiL))tanh(2Pih/L)]^1/2, where g is the acceleration due to gravity, L is the distance between wave crests, and h is the depth of the water. Get an equation for the rate of change of f with respect to h assuming g and L are constants.

Well this is what I've gotten so far...I'm not sure if it is right or not...

df/dh=1/2((g/2PiL) tanh(2Pih/L))^-1/2 * ((g/L^2)sech^2(2Pih/L))

=((g/L^2)sech^2(2Pih/L))/2√((g/2PiL)tanh(2Pih/L))

well seems that the final answer is

(gPi/2L^3)^1/2 csch^1/2(2Pih/L)sech^3/2(2Pih/L)

So, I have no idea how this answer was derived, looking at it seems that they integrated it (sech^3/2)... is that so?

It would be of great help you anyone could give a hand on this one....

Thank you so much... guys...

In shallow ocean water, the frequency of the wave action (number of wave crests passing a given point per second) is given by f= [(g/(2PiL))tanh(2Pih/L)]^1/2, where g is the acceleration due to gravity, L is the distance between wave crests, and h is the depth of the water. Get an equation for the rate of change of f with respect to h assuming g and L are constants.

Well this is what I've gotten so far...I'm not sure if it is right or not...

df/dh=1/2((g/2PiL) tanh(2Pih/L))^-1/2 * ((g/L^2)sech^2(2Pih/L))

=((g/L^2)sech^2(2Pih/L))/2√((g/2PiL)tanh(2Pih/L))

well seems that the final answer is

(gPi/2L^3)^1/2 csch^1/2(2Pih/L)sech^3/2(2Pih/L)

So, I have no idea how this answer was derived, looking at it seems that they integrated it (sech^3/2)... is that so?

It would be of great help you anyone could give a hand on this one....

Thank you so much... guys...