The Second Derivative (1 of 3: Introducing Terminology)

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[@jeongin5041]

wow. i cannot begin to explain how much this has helped me. thank you!

[@xAuroraNova]

I love your lectures. I just finished calculus 2 at uni, but reviewing some questions I had and this perfectly explained a notion that baffled me at first. Thanks!

[@lalithmathotage871]

Great sir❤

[@shreyans2224]

thnks sir for helping me for my exams....🙏

[@matemaatika-math]

As in "dx", both "d" and "x" appear twice, why don't we write "d ^ 2 * x ^ 2" and write only "d * x ^ 2"?

[@smrpkrl]

that's dx whole squared

[@matemaatika-math]

@@smrpkrl How is it squared? It's not a multiplication. It's a function of a function. You can't tell that sin(sin(angle)) is (sin(angle)) ^ 2, can you?

[@yupitzmeeee]

Its delta x ^2 . So whatever delta x is times delta x. Its the same thing mate.

[@carultch]

​@@matemaatika-math It doesn't necessarily mean that the operation is squared. It's just the notation we use. The implication is that there are two copies of d in the numerator, and two copies of dx in the denominator. We note it as squared as a shorthand, regardless of whether it really has anything to do with squaring. The implication is d^x y / (dx)^2, and we just don't bother to parenthetically enclose dx, since it is implied, and we would rarely (if ever) "square" the x without also squaring the d.

[@morrman3350]

wooo :D