Derivatives
Chapter Name : Limits And Derivatives |
Sub Topic Code : 104_11_13_05_02 |
Topic Name : Derivatives |
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Sub Topic Name : Algebra Of Derivative Of Functions |
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Introduction
• In day to day life there are many applications in which quantities associated with some process are linked with some other quantity. • Change in one quantity will result in change in related quantity also. • Algebra of derivatives can be applied to determine the rate of change of quantities.
Pre-Requisites:
Knowledge of algebraic functions and derivatives.
Activity:
You will observe as you increase volume of balloon the other two quantities also change.
Real Life Question:
A Petrol tank is being filled with petrol through pipes. The volume of petrol in tank at any given time is given by V (t) = 2+5t-10t². Find the rate at which volume is increasing when t=1.
Key Words / FlashCards
| Key Words | Definitions (pref. in our own words) |
|---|---|
| Derivative | Rate of change of one physical quantity with other. |
| Algebra | Algebra is used to represent number and quantities in equation. |
Learning aids / Gadgets
| Gadgets | How it can be used |
|---|---|
| Balloon | Fill balloon with air at a constant rate. If the ratio of length of balloon to its radius is fixed. At what rates do the length and radius of balloon change? |
Real life uses :
Derivatives are used in applications that rely on speed, to find population growth, in stock market.
Places to visit :
Fill bottle with water from water filter and find the rate at which volume of bottle is increasing.
Practical examples around us
| Examples | Explainations |
|---|---|
| Petrol Tank | If the volume of petrol tank is given in terms of polynomial. If we differentiate the polynomial with respect to time t then we can get the rate at which the volume is increasing. To find this we apply rules of derivatives. |
What you learn in Theory:
Theoretically derivatives have some rules with the help of these rules problems on derivatives can be solved.
What you learn in Practice:
For example, as volume of cylinder depends on height and radius of cylinder. If we change one quantity the other two quantities also change. Product rule of derivative can be applied to know how the change in one quantity will affect other quantity as well.