Differentiability
We have already defined the derivative of a function f(x) at a particular point 'a' and derivative of f(x) in general for the variable x as f'(a) and f'(x) respectively. The restriction in both the cases is that 'the limit must exist'. If does n..
We have already defined the derivative of a function f(x) at a particular point 'a' and derivative of f(x) in general for the variable x as f'(a) and f'(x) respectively. The restriction in both the cases is that 'the limit must exist'. If does n..Differentiability
>does not exist, then we say that the function is not differentiable. If the above limit exists, we say the function f(x) is differentiable. In order to test the differentiability of a function at a point, the right hand derivative and left hand derivatives a..
Derivability or Differentiability at a Point
Let f be a function and a be any point in its domain. Let h>0 be a small number. f(x) is said to be differentiable if exists and is denoted by f | (a), then f | (a) is called the derivative or differential coefficient of f(x) at x = a. That ..
Let f be a function and a be any point in its domain. Let h>0 be a small number. f(x) is said to be differentiable if exists and is denoted by f | (a), then f | (a) is called the derivative or differential coefficient of f(x) at x = a. That ..The slope field and graphical solution of a differential equation is s..
The slope field and graphical solution of a differential equation is shown. Which of the following is that differential equation? => d y d x = 2 x or d y d x = - 2 or d y d x = 2 or d y d x = 1 ..
The slope field of a certain differential equation is shown. Which of ..
The slope field of a certain differential equation is shown. Which of the following is the solution to that differential equation? => y = - 1 x + C or y = x 2 + C or y = ( x 2 + C ) 1 2 or y = ( x 3 + C ) 1 3 ..
Logarithmic Differentiation
When we want to differentiate a function of the form f(x) g(x), we use logarithmic differentiation.When we want to differentiate a function of the form f(x) g(x), we use logarithmic differentiation. Let y = f(x..
When we want to differentiate a function of the form f(x) g(x), we use logarithmic differentiation.When we want to differentiate a function of the form f(x) g(x), we use logarithmic differentiation. Let y = f(x..Approximations by Differentials
Approximations by Differentials - Let y = f (x) be a differentiable function of x, errors in x and y are denoted by d x and d y, we have \ Error in y = f ' (x) d x..
Approximations by Differentials - Let y = f (x) be a differentiable function of x, errors in x and y are denoted by d x and d y, we have \ Error in y = f ' (x) d x..Differentiation from First Principles
Let y = f (x). The derivative of f at x is denoted by f '(x). Finding the derivative of a function using the above definition is called differentiation from first principle..
Let y = f (x). The derivative of f at x is denoted by f '(x). Finding the derivative of a function using the above definition is called differentiation from first principle..Introduction to Differentiation
Introduction to Differentiation - After having studied functions, limits and continuity in the previous chapter, we shall further divide the class of continuous functions into two sub classes, derivable and non-derivable.After having studied functions, limits and continuity in t..
Differentiability at a Point
A function f(x) is said to be differentiable at a point 'a' if (i) both Rf '(a) and Lf '(a) exists and finite. (ii) Rf '(a) = Lf '(..
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