Equity is equal to total assets minus its total liabilities. These figures can all be found on a company's balance sheet for a company. It shows the ownership in the Company. 

A derivative is a formal financial contract that allows an investor to buy and sell an asset for a future date. The expiry date of a derivative contract is fixed and predetermined. Derivative trading in the share market is better than buying the underlying asset since the gains can be substantially inflated.

Moreover, derivative trading is a leveraged form of trading, meaning you can buy a large quantity of the underlying assets by paying a small amount. You can trade in different types of derivatives, such as stocks, commodities, currencies, benchmarks, etc.

Derivative contracts are of two types - futures and options. In essence, both are the same since the investor, and the seller predicts the price of the underlying asset for a specific future date. But, futures and options are different in that, in futures, both the buyer and seller are under the legal obligation to honour the contract on expiry.

However, in the case of options, the buyer or seller can buy/sell before expiry by exercising their rights or letting the contract expire without any exercise of rights. Options are of two types - Call option and Put option. Investors buy a Call option when they are confident that the underlying asset will go up. In contrast, they buy a Put option when they feel certain that the price of the underlying asset will come down.