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The purpose of finding a derivative is to find the instantaneous rate of change. In addition, taking the derivative is used in integration by parts.
By the product rule. d/dX(pitanX) = pisec2X ----------------
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.
If that is a simple product, just use the product rule. If there is a power involved - that is not always clear in the question - you must use logarithmic differenciation.
The product rule for derivatives is as follows. For the derivative of the product of two functions, "f" and "g":(f times g)' = f times g' + f' times g