In derivatives, the quotient rule is a procedure of finding that is the ratio of two differentiable functions. Let, f(x) =g(x)/h(x), whereas both the g and h are known as differentiable and h(x)≠0. The quotient rules also look out the derivative of f(x) is,
For calculation of derivative relating to the question of two different function formula of quotient rules in the form of derivate is used:
In this formula, d denotes as a derivative. So dg (x) means the derivative of function g and df(x) means the derivative of function f. the formula states that to find the derivative of f(x) divided by g(x),
Let’s take the g(x) is the times of derivative of f(x). After that the product, we must subtract the product of f(x) times the derivative of g(x). And finally, we can divide those terms by g(x) squared.
So, Derivatives is a financial security whose value is derived from an underlying assets. The underlying assets can be equity, index, foreign exchange, commodity, and any other assets. In the particular derivative market there are three derivative, the derivative are hedger, speculator and arbitragers. Hedgers are the face risk associated with the price of an asset. They use futures or option markets to reduce or animations their risk. Then another particular derivative market is speculator, speculator bet on the future movements in the price of an assets. Then the last derivative market is arbitrages market, in this market arbitrages make profit by taking advantages of difference between prices of the same product across different markets. So suppose there are two market, market A and market B, there are also a particular product, suppose the product is X, if the price is market A is Rs 10, and the price is market B is Rs. 15, then the arbitrages buy the product in Rs 10 in market A and sell the product market B in Rs 15, so he will gain Rs. 5.
The type of the derivative market: first one the commodity derivative market and secondly the financial derivative market. In commodity market contracts in which underlying asset in a commodity, like agriculture commodity like wheat, cotton etc. precious metals like gold, silver etc. energy products like crude oil, natural gas, cool etc. And another one is financial derivative market, in this market contract in which underlying asset is a financial asset, like equity, interest return and exchange rates. There are some types of derivative contracts: forward, future, option and swap. Option again divided by two types call option and put option. Swap also divided by two type’sinterest rate swap and currency swaps.
Forward contract is an agreement between parties to buy and sell the underlying assets at a specific date and agreed rate in future and in the case of future contract in which the parties agree to exchange the assets for each at a fixed price and at future specific date, is known as future contract. So the forward contract is a customized contract and future contract is a standardized contract. As well as the forward contract traded on over the counter i.e, there is no secondary market and in future contract traded on organized stock exchange.
An option is a contract, which given the right, but not an obligation, to buy or sell the underlying at a stated date and at a stated price. While a buyer of an option pays the premium and buyer the right to exercise his option, the writer of the option is the one who receive the option premium and therefore, obliged to sell/buy the asset, if the buyer exercises it on him. Already we said that option are two types. In call options gives the buyer the right, but not an obligations to buy a given Quantity of the underlying asset, at a given price on or before a given future date. And in put option givesthe buyer the right, but not an obligations to sell a given Quantity of the underlying asset, at a given price on or before a given future date. For example, European option, in this option exercised only on the date of option expiry. And in case of American option exercised at any time before the option expire.
In derivative contracts the last one is swap contract, these are private agreements between two parties to exchange cash flows in the future according to the formula. Swaps are commonly used- interest rate swaps and currency swap. These entail swapping only the interest related cash flows between the portions in the same currency. And in case of currency swaps entail swapping both principal and interest between the parties, with the cash flow in one directions being in a different currency than those in the opposite directions.
Derivatives of quotients (quotient rule):
In other words, to derive the derivatives of a product we cannot consider the product of that derivatives. We can use the same formula and we can do the same thing in quotients. Example of quotient rules are:
For the above calculation using the derivative formula to ascertain the solution. At first multiplying both the side with (x+1) we got 1st phase of the calculation. After the required subtracted we got the solutions..
For the above calculation using the derivative formula to ascertain the solution. At first multiplying both the side with (x-1) we got 1st phase of the calculation. After the required subtracted we got the solutions.
Some others example of quotient rules are:
In quotient rules, there is a similar rule for quotients. To prove it, we go to the definition of the derivative:
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