A derivative can be defined as something which derives its value from an underlying product being a stock, currency, commodity or anything that carries a market price.
The market price of a product is subject to fluctuations due to various factors effecting its demand & supply thereby associating itself to various risk factors.
SO, derivative is a by-product of the core product which can be used to hedge, speculate & also undertake arbitrage activities.
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If by "2aXaXa", you actually mean "2a3", then the derivative with respect to a is 6a2. On the other hand, if you actually mean "2a3X2", then it's derivative with respect to X would be 6a2X2(da/dx) + 4a3X. If "a" is simply a constant though, then it's derivative is 4a3X
It means that the first derivative is a constant. The derivative may be with regard to time or any other variable.
"Derivative of"
The derivative of a curve is basically the slope of the curve. If we say, for example, that if y = 2x, the derivative is 2, that means that at any point the line has this slope. If we say that for the function y = x2, the derivative is 2x, that means that at any point "x", the slope is twice the value of "x".
well, the second derivative is the derivative of the first derivative. so, the 2nd derivative of a function's indefinite integral is the derivative of the derivative of the function's indefinite integral. the derivative of a function's indefinite integral is the function, so the 2nd derivative of a function's indefinite integral is the derivative of the function.