derivations


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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. This function in w..
Derivative of Exponential Function
If f(x) = e x , then ..
Derivative of sin x
Let f(x) = sin x. Then, we have ..
Derivative of sec x
Let f(x) = sec x. Then, we have Similarly, we can prove that..
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 range of these functions are tabulated below.Before finding the..
Left Hand Derivative
The LHD of f at a is defined as where h>0, 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. This functio..
Derivation of the First equation of motion
Consider a particle moving along a straight line with uniform acceleration 'a'. At t=0, let the particle be at A and u be its initial velocity and when t = t, v be its final velocity. v = u + at I equation of motio..
Derivation of the First Equation of Motion
Consider a particle moving along a straight line with uniform acceleration 'a'. At t = 0, let the particle be at A and u be its initial velocity and when t = t, v be its final velocity. v = u + at I equation of motio..
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