"Derivatives are functions that give you the slope of an original function at some value... very useful for calculating rates of change."
"What are you doing when you're finding a derivative? What are you finding? That's what a derivative represents."
"You're finding the slope of a curve at a point, that's the derivative function."
"Warren Buffett calls derivatives financial weapons of mass destruction."
"During abnormal times, derivatives markets can exacerbate these kinds of Market dislocations."
"Derivatives are financial weapons of mass destruction... Blythe Masters is one of the destroyers of the world."
"Imagine freeing up the entire derivatives market."
"This instantaneous slope is also the derivative."
"The key to why the e to the X function and also functions like sine of X and cosine of X equal their tailor series is because their higher order derivatives grow much slower than an N factorial as you increase the derivative order n."
"If a complex valued function merely has a first derivative on some open region of the complex plane, then it automatically has all higher order derivatives on that region too."
"We know that e to the z is its own derivative so if I were to zoom into a point z the transformation would look like being multiplied by e to the z."
"Everything we use at some point is going to be a derivative of some kind of animal."
"Critical points for single variable calculus occur where the first derivative of the function is equal to 0 or is undefined."
"If d is positive and the second partial derivative with respect to x is negative, then f has a local maximum at x naught y naught."
"The bottom times the derivative of the top minus the top times the derivative of the bottom."
"After you learn derivatives, you should learn applications, right? Applications of the derivative."
"Derivatives are everywhere, and there are some examples that I've given you here, but this is an area which is considered rocket science because of the analytics that are so demanding."
"One of the 106 chosen as it's the exact same number as the original McLaren F1s of all different derivatives."
"So the whole idea here, it's very different. We try to manage big portfolios of derivatives, and we try to price them and charge a little bit extra so that we can make our living, but on the other hand, we don't take any risk."
"...a contango means that the derivative is trading higher than the price of the asset itself, and when it's in backwardation, it means it's trading lower."
"Since VIX Futures and VIX options both settle to the same number, their prices will always be in line with each other."
"Apply the fundamental theorem to find derivatives, just like magic!"
"We took the derivative algebraically and got a closed form solution without ever having to use the piecewise definition."
"And we found the derivative without referencing inverse functions or knowing anything about the derivative of e to the X itself."
"There is a precise sense in which you think about derivatives in the sense of calculus, derivations, and these boundary operators."
"this is one half times x to the negative one and when you do the second derivative just use the power rule so the negative one comes down to make negative half X and you subtract one to the negative two and that's still going to work out to this"
"Your job is to find all those derivative values like the f of 1, f prime of 1, f double prime."
"A swap is a financial derivative in which two counterparties exchange the cash flow of one party's financial instrument for those of the other parties financial instrument for a period of time stated in the agreement."
"Credit default swap provides insurance against the risk of a possible default on a debt."
"The primary objective of weather derivatives is to hedge the volume risk rather than the price risk."
"Why are we talking about an LSD precursor then? Well, lysergic acid derivatives such as bromocriptine and perlitazone are actually used in the treatment of early stage Parkinson's disease or type 2 diabetes."
"Deribit owns the market from a derivatives perspective."
"Differentiation has key derivatives that you must make sure you know."
"These two we just looked at, interest rate guarantees and FR a's, they're what we call OTC or over-the-counter."
"A partial differential equation or a PDE is basically an equation involving one or more derivatives of an unknown function of two or more independent variables."
"The most common type of relationship that we look at between the original function, the first derivative, and the second derivative is the relationship between position, velocity, and acceleration."
"If we take what's called the covariant derivative, it's a derivative of a vector."
"It's so important now to be able to take derivatives."
"Replication refers to the creation of an asset or a portfolio by using a combination of other assets or portfolios with derivative securities."
"If you're going to do calculus, the next thing is what about the derivatives of the function. How does it change?"
"Derivatives are used to manage risk."
"The derivative of f of x is the limit as h tends to zero."
"Derivatives are very important for training neural networks; they're how we do backpropagation and update the parameters of neural networks."
"As we allow Delta X to approach zero and take the limit, that difference becomes a derivative."
"When you deal with functions or data, taking the derivative depends on the scenario."
"Derivatives are all about how things change, the rates of change of functions."
"It allows us to price derivatives that are sensitive to implied volatility smiles and skews."
"Derivatives derive value from an underlying, will be settled at a future date, and the amount paid initially is nil or insignificant."
"Next lecture, we're going to get into how to take the derivatives of complex value functions when we can and cannot do it."
"Derivatives are measured at FVPL, of course, and that makes perfect sense."
"The greatest derivative that appears is the first derivative."
"The derivative of a polynomial is the polynomial with the coefficients moved up one degree."
"This has the advantage of the derivative of \( r \) over \( r \) equaling the negative derivative of \( u \) over \( u \)."
"The derivative of four position s is another four-dimensional vector containing derivatives of t, x, y, and z with respect to proper time tau."
"Differential equations involve derivatives, and our solutions are equations themselves."
"To find the derivative of a function for a given input value is one of the essential skills for AP calculus."
"To find the derivative at a point, we use the nDeriv function."
"The derivative of the function x is equal to 1 always."
"The derivative of the whole thing is the sum of derivatives of each term."
"If derivatives represent slopes and you have a differential equation with the derivative in it, then we have a formula to find slope at any point."
"If \( f(z) \) is analytic at that zero, then derivatives of all orders are also analytic at zero."
"We're going to continue our discussion on weather derivatives and specifically temperature options."
"The velocity is the derivative of position, or more specifically, v of t is equal to the s prime of t."
"The limit of the derivatives is equal to the limit of the fraction of the functions themselves."
"It's the difference between showing someone the derivative of the function and then explaining that what you're doing is finding a function that gives you the slope of a function at that point."
"Even if you're using the computer to take derivatives, you really have to have some idea of what's going on under the hood."
"The derivative is taking a non-linear function and pretending at least locally that it's a linear function."
"The idea that a derivative is taking a non-linear function and pretending at least locally that it's a linear function."
"If the variable represents the first derivative, then the derivative of that variable would represent the second derivative."
"If the first derivative is P itself, the derivative of P would represent the second derivative of Y."
"The derivative of f(x) is equal to 4x-3."
"The solution of an nth order differential equation must always have at least n derivatives."
"The derivative of y with respect to x is y prime."
"What will I do? Well, I can use various derivative products like interest rate futures, interest rate forwards, caps or floors which are options, or even interest rate swaps."
"The derivative of our function is equal to something that we're looking for."
"It involves derivatives, and the terms will get smaller and smaller."