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Instantaneous Rate of Change Formula Instantaneous Rate of Change Formula At the particular point, the rate of change is called as instantaneous rate of change ,which is same as the derivative values at the same point. If we consider a function, this rate of change at a particular point is same as slope of the tangent line at the same point which is the slope of the curve. When the object is travelling along a straight line, Average velocity is the average rate of change of place with respect to time. This method is known as differentiation with the fundamental theorem of calculus: lim as h->0 of f(x + h) = ( f(x + h) - f(x) ) / h There have been rules that have been formed by this formula, depending on the type of function given. Note: ' shows it is the rate of change function: Some basic rules: y = ax^n (where a is just a constant) y' = n ax^(n - 1) where n 0 Product rule: y = f(x)g(x) y' = f'(g)g(x) + f(x)g'(x) Quotient rule: y = f(x)/g(x) y' = [f'(g)g(x) - f(x)g'(x)] / [g(x)]^2 Chain rule: y = f(g(x)) y' = f'(g(x))g'(x) Natural Logarithms: y = ln f(x) y' = f'(x) / f(x) Exponential (base e) y = e^f(x) y' = f'(x)e^f(x) Trigonometric: y = sin f(x) y' = f'(x) cos f(x) y = cos f(x) y' = -f'(x) sin f(x) y = tan f(x) y' = f'(x) [sec f(x)]^2 y = cosec f(x) y' = -f'(x) cot f(x) cosec f(x) y = sec f(x) y' = f'(x) tan f(x) sec f(x) y = cot f(x) y' = -f'(x) [cosec f(x)]^2 Know More About Definition of Integration

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To evaluate limits with sums/differences involving square roots {you ought to know that 1/ (x+2) ^1/2 is 1/√(x+2) } just multiply top and bottom by the conjugate (change the sign of one square root). The rest is routine algebra: multiply, simplify (I hope you can subtract fractions), reduce and substitute h=0. Eventually you will learn some "derivative rules", which reduce the algebra required. However, in my class you have to prove that you can do enough algebra to prove the derivative rules before you are allowed to use them! Last section we discovered that the average rate of change in F(x) can also be interpreted as the slope of a scant line. The average rate of change involves the change in F(x) over a designated interval [x1, x2] or between the two points (x1, F(x1)) and (x2, F(x2)). The secant line passes through these two points. A logical extrapolation would indicate that the instantaneous rate of change in F(x) at a point x would be the same as the slope of a tangent line touching the graph of F(x) at that same point (x, F(x)). In the case of average rate of change you can find the slope of the secant line easily because you have two points to work with. But in the case of the instantaneous rate of change there is only one point and therefore it is not possible to directly calculate the slope of the tangent line. Is it possible to find this value that will be both the slope of the tangent line and the instantaneous rate of change? We will now define a process that will help us do just that. We would like the find the instantaneous rate of change in profit for q = 40. We will find the instantaneous rate of change numerically. This method proceeds as follows: Since we can not find the slope of the tangent line touching the graph at q = 40 by direct calculation we will try to guess its value as precisely as possible. In order to do this we must find slopes of secant lines that are very close to the tangent line at the point.

Learn More How to do Integrals

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What is Derivative What is Derivative Definition of Derivative: The main tool that is used in differential calculus is called the derivative. Let the given function is denoted as y = f(x). If the independent variable changes from the value ‘x’ to another value x + x0 then x0 is called an increment of ‘x’. Similarly y0 denotes an increment in ‘y’. If ‘x’ changes x + x0 then the function y = f(x) will change from ‘y’ to y + y0 so that. A financial instrument whose characteristics and value depend upon the characteristics and value of an underlier, typically a commodity, bond, equity or currency. Examples of derivatives include futures and options. Advanced investors sometimes purchase or sell derivatives to manage the risk associated with the underlying security, to protect against fluctuations in value, or to profit from periods of inactivity or decline. These techniques can be quite complicated and quite risky. Derivatives are financial contracts that are designed to create market price exposure to changes in an underlying commodity, asset or event. In general they do not involve the exchange or transfer of principal or title. Rather their purpose is to capture, in the form of price changes, some underlying price change or event.

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The term derivative refers to how the price of these contracts are derived from the price of some underlying security or commodity or from some index, interest rate, exchange rate or event. Examples of derivatives include futures, forwards, options and swaps, and these can be combined with each other or traditional securities and loans in order to create hybrid instruments or structured securities I below for a primer on derivative instruments). Derivatives are traded on derivatives exchanges, such as the Chicago Mercantile Exchange which employs both open outcry in "pits" and electronic order matching systems, and in overthe-counter markets where trading is usually centered around a few dealers and conducted over the phone or electronic messages. Derivatives play a useful and important role in hedging and risk management, but they also pose several dangers to the stability of financial markets and thereby the overall economy. In broad sense, the derivative of a function may be defined as the ratio of the change of value of the function for a given change of the input variable. At first, this definition may look exactly same as the definition of the slope of the function. It is true in case of linear functions, where the slope is constant throughout the domain. Hence, the derivative of the function is nothing but the slope of the function in such cases. However, the slope of all functions may not be constant in their domains. Therefore, in these cases, the slope at any particular point is defined as the derivative of the function.

Read More About What is Function Notation

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Instantaneous Rate of Change Formula  

When the object is travelling along a straight line, Average velocity is the average rate of change of place with respect to time. At the pa...

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