inverse functions and their derivatives


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Derivative of Inverse Trignometric Functions
Derivative of Inverse Trignometric Functions - Before finding the differentiation of inverse trigonometric functions, recall how the inverse trigonometric functions are defined and what the domain and range of each inverse..
Derivative of Inverse Trignometric Functions
Before finding the differentiation of inverse trigonometric functions, recall how the inverse trigonometric functions are defined and what the domain and range of each inverse trigonometric function. For ready reference, the domain and ran..
Derivative of a Function
So far we have discussed the derivative of a function f(x) at a point 'a' which is in the domain of f. Suppose we want to find the derivative of the same function at a different point 'b', then we have to compute the derivative by repeating the same..
Inverse Functions
Let f : A B be a real valued one-one and onto function. Therefore, we can define a function, (denoted by f - 1 ) called 'the inverse of f ' as follows: f - 1 : B A such that..
Derivative of a Function of a Function
The differentiation of function of a function is known as 'chain rule'. The chain rule is probably the most widely used differentiation rule in mathematics. If y is a differentiable function of u and u is a differentiable function of x, then the h..
Derivative of a Function of a Function
So far, we know how to differentiate functions like sin x and x 3 - 5. But how do we differentiate a function of a function? That is how can we differentiate sin (x 3 - 5)?So far, we know how to differentiate functions like sin x and x 3 - 5. But how do we di..
Derivative of Some Important Functions
The Derivative of Some Important Functions are: 1. Derivative of a Constant, 2. Derivative of x n where n is any integer, 3. Derivative of a Constant of a Function, 4. Derivative of Exponential Function..
Notion for the Derivative of a Function
The derivative of the function f with respect to a variable x is the function f ' whose value at x is provided the limit exist..
Derivative of Implicit Functions
Till now, the functions that we have discussed, are explicitly functions of x. We have defined y in terms of x. Suppose we have an equation f(x,y) = 0, which cannot be put in the form of y=f(x) to differentiate in the usual way, we can still differentiate the equation f(x,y) = 0..
Derivative of a Constant of a Function
Let f (x) = k u(x) where k is a constant and u = u(x), x R, be a differential function of x. We then have ..
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