Calculus 1 CH 5.2 Second and Higher Order Derivatives (3 of 11) Notation

Given: f(t)=x f(t)=t^3+5t^2+6t+4 x(t)= t^3+5t^2+6t+4
We will find the first, second, third, fourth, and fifth derivative with respect to t:
f’=f’(t)=x’=x’(t)=?
f”=f”(t)=x”=x”(t)=?
f’’’=f’’’(t)=x’’’=x’’’(t)=?

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[victorf]

You are doing God's work professor. Thank you. I love these math lectures

[conzopontsho]

I performed well in my University Math because of professor.

[delphitechledlighting]

Professor - I've been enjoying your lectures. Excuse me for commenting here but I'm doing it because I wasn't able to find an email to reach out to you on and I'm reaching out here since this video was just posted by you minutes ago and I presume you or one of your helpers may be monitoring comments. To the point, I've been looking at some of your lectures relevant to GHG computations. Although my work doesn't involve anything to do with climate modeling, with my curiosity and physics education I've taken on a hobby to try and do some photonic calculations with what I think may be a fresh approach to evaluating the impact of rising CO2 levels. As you point out in your video "Astronomy - Ch. 9.1: Earth's Atmosphere (45 of 61) What Does the CO2 Absorption Spectrum Imply?" the side-band is where the impact occurs. So I'm seeking fine grained measured results across the full relevant bands of interest from the furthest edges of the full band where the slightest resonance begins.

I've looked at RADIS/HITRAN simulations for various GHGs, in particular CO2, N2O, and CH4 are of interest. Those simulations are shown as logarithmic plots of absorption coefficient versus wavelength spanning 2um to 20 um. The HITRAN organization recommends that measured results should always be used where accuracy counts and I'm looking for fine grained tabular data for the spectrum of interest. If automated perhaps a full sweep of 2um to 20um akin to the HITRAN graphs with many points per um to capture some points on some of the steepest slopes of the HITRAN plots (50ish data points per um would be great). However, I'd be happy just to get the 4.3 um and 15 um band data spanning what is shown in those plots. I figured for at least CO2, I'd readily find such data somewhere on the internet but despite considerable searching, I've come up empty. One would think that with decades of modeling the effect of CO2, that data would have been useful to many and would be easy to find.

Do you know of any organization where they may have the data or can produce the data that I'm looking for, at least for CO2 as a starting point? Should some organization have the lab setup to produce tabular data akin to those plots I've referenced, I'll be pleased to collaborate with them and credit them with the source of the data as I plan to publish once I complete my computations.

Thank you again for your excellent lectures. I'd be excited if you can help me find a data source or can point me to a lab willing to perform the measurement and provide me with them. All the best, Rodney

[allenofatlanta]

I never realized that there were so many ways to express different derivatives.
However, to this day I’m still confused about end notation " dx/dt." It is not a rational expression. What exactly is it?