derivatives of composite functions

Let f : A g B and g : B g C be two functions. Let h: A g C be function such that h(x) = g(f(x)) h is called the composite of f and g, denoted by h = g o f. i.e., (g o f) (x) = g (f(x..

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 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..

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 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 ..

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..

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..

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..

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 ..