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Page 1 STROUD Worked examples and exercises are in the text Programme 8: Differentiation applications Differentiation of inverse trigonometric functions Derivatives of inverse hyperbolic functions Maximum and minimum values Points of inflexion Page 2 STROUD Worked examples and exercises are in the text Programme 8: Differentiation applications Differentiation of inverse trigonometric functions Derivatives of inverse hyperbolic functions Maximum and minimum values Points of inflexion STROUD Worked examples and exercises are in the text Programme 8: Differentiation applications Differentiation of inverse trigonometric functions Derivatives of inverse hyperbolic functions Maximum and minimum values Points of inflexion Page 3 STROUD Worked examples and exercises are in the text Programme 8: Differentiation applications Differentiation of inverse trigonometric functions Derivatives of inverse hyperbolic functions Maximum and minimum values Points of inflexion STROUD Worked examples and exercises are in the text Programme 8: Differentiation applications Differentiation of inverse trigonometric functions Derivatives of inverse hyperbolic functions Maximum and minimum values Points of inflexion STROUD Worked examples and exercises are in the text Programme 8: Differentiation applications Differentiation of inverse trigonometric functions If then Then: 1 sin yx ? ? sin and so cos y dx x y y d ?? 2 2 1 / 1 cos 1 1 sin 1 1 dy dx dx dy y y x ? ? ? ? ? ? ? ? 1 2 1 sin 1 d x dx x ? ? ? Page 4 STROUD Worked examples and exercises are in the text Programme 8: Differentiation applications Differentiation of inverse trigonometric functions Derivatives of inverse hyperbolic functions Maximum and minimum values Points of inflexion STROUD Worked examples and exercises are in the text Programme 8: Differentiation applications Differentiation of inverse trigonometric functions Derivatives of inverse hyperbolic functions Maximum and minimum values Points of inflexion STROUD Worked examples and exercises are in the text Programme 8: Differentiation applications Differentiation of inverse trigonometric functions If then Then: 1 sin yx ? ? sin and so cos y dx x y y d ?? 2 2 1 / 1 cos 1 1 sin 1 1 dy dx dx dy y y x ? ? ? ? ? ? ? ? 1 2 1 sin 1 d x dx x ? ? ? STROUD Worked examples and exercises are in the text Programme 8: Differentiation applications Differentiation of inverse trigonometric functions Similarly: ? ? 1 2 1 cos 1 d x dx x ? ? ? ? ? ? 1 2 1 tan 1 d x dx x ? ? ? Page 5 STROUD Worked examples and exercises are in the text Programme 8: Differentiation applications Differentiation of inverse trigonometric functions Derivatives of inverse hyperbolic functions Maximum and minimum values Points of inflexion STROUD Worked examples and exercises are in the text Programme 8: Differentiation applications Differentiation of inverse trigonometric functions Derivatives of inverse hyperbolic functions Maximum and minimum values Points of inflexion STROUD Worked examples and exercises are in the text Programme 8: Differentiation applications Differentiation of inverse trigonometric functions If then Then: 1 sin yx ? ? sin and so cos y dx x y y d ?? 2 2 1 / 1 cos 1 1 sin 1 1 dy dx dx dy y y x ? ? ? ? ? ? ? ? 1 2 1 sin 1 d x dx x ? ? ? STROUD Worked examples and exercises are in the text Programme 8: Differentiation applications Differentiation of inverse trigonometric functions Similarly: ? ? 1 2 1 cos 1 d x dx x ? ? ? ? ? ? 1 2 1 tan 1 d x dx x ? ? ? STROUD Worked examples and exercises are in the text Programme 8: Differentiation applications Differentiation of inverse trigonometric functions Derivatives of inverse hyperbolic functions Maximum and minimum values Points of inflexionRead More
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FAQs on PPT: Derivatives & Their Application - Engineering Mathematics - Civil Engineering (CE)
| 1. What are derivatives and how are they used in finance? |  |
Derivatives are financial instruments that derive their value from an underlying asset. They are commonly used in finance to hedge risks, speculate on market movements, and provide leverage. For example, options and futures contracts are types of derivatives that allow investors to bet on the price movements of stocks, commodities, or other assets without owning the underlying asset.
| 2. What are the different types of derivatives? | |
There are several types of derivatives, including options, futures contracts, forwards, swaps, and credit derivatives. Options give the holder the right, but not the obligation, to buy or sell an asset at a predetermined price within a specific time frame. Futures contracts oblige the parties involved to buy or sell an asset at a predetermined price on a future date. Forwards are similar to futures but are traded over-the-counter. Swaps involve exchanging cash flows or liabilities based on predetermined terms. Credit derivatives are specifically designed to manage credit risk associated with debt instruments.
| 3. How can derivatives be used to manage risk? | |
Derivatives can be used to manage risk by providing a means of hedging against adverse price movements. For example, a farmer can use a futures contract to lock in a price for a future crop harvest, protecting against potential price fluctuations. Similarly, investors can use options to limit losses in their investment portfolios or to protect against currency exchange rate fluctuations when trading internationally.
| 4. Are derivatives only used by institutional investors? | |
No, derivatives are not limited to institutional investors. While institutional investors, such as banks and hedge funds, are significant users of derivatives due to their complex risk management needs, individual investors can also participate in the derivatives market. Many retail brokerage firms offer options and futures trading accounts to individual investors, allowing them to access these financial instruments.
| 5. What are the potential risks associated with derivatives? | |
Derivatives can involve a certain level of risk due to their leverage and complexity. If not properly understood or managed, derivatives can result in substantial losses. Investors can lose more than their initial investment, especially with leveraged derivatives like futures contracts. Additionally, derivatives markets can be highly volatile and subject to sudden price movements, which can lead to significant financial losses. Therefore, it is important for investors to have a thorough understanding of derivatives and to use them prudently.
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