subject: Derivatives Using Limits [print this page] What is Derivative? What is Derivative?
The word differentiation means that its value is dependent on some other source, function or value. Finding differentiation is an important operation in Mathematics, especially in differential calculus. The trigonometric derivatives are found out or calculated from trigonometric functions using differentiation process.
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Definition of Derivative
If the trigonometric function is given by a = g(x), then its differentiation is denoted by a or g(x). This trigonometric differentiation and trigonometric function is based on the variable x. The process of calculating the differentiation is termed as differentiation. Differentiation is represented as shown below:
da d
a = g(x) = ------ = ----- (g(x))
dx dx
Derivatives Using Limits
Using limits implies the process of evaluating the given expression when the limit is approached. By using these limits, the differentiation can be properly estimated and perfect answer i.e. differentiation is obtained.
Finding out derivatives using limits is possible by applying the following formula:
g(x+n) g(x)
a = lim ------------------
n implies 0 n
This is calculated by subtracting the g(x) from g(x+n) and then dividing the result by n, where n represents the limit, nimplies0. The range of difficulty of differentiation using limits extends from easy to complex. By properly using the algebra and functional notation, the differentiation can be easily obtained.
If the value of n limits to some value c, then the differentiation using limit definition is given by:g(n) g(c)a = lim ------------------ n implies c n-cProperties of differentiationThe differentiation shows the effect of change of input. As the input changes, the corresponding output also changes. Here are certain important properties of differentiation:If there are two functions f(a) and f(b) and there is a real number n, then by applying it in the differentiation formula, we get n(f(a)) = n(f(a))The differentiation of the real number is zero.The differentiation of the summation of any two functions will be equal to the sum of the differentiation of the two functions.Similarly, the differentiation of the difference of any two functions will be equal to the difference of the differentiation of the two functions.Derivatives of Inverse functionsDerivative of sin inverse a is given by one divided by square root of one minus square of a. Multiplying the result of sin inverse a by -1 will fetch the derivative of cos inverse a. The derivative of tan inverse of variable a is given by one divided by the sum of a and the square of a.by: Omkar Nayak
