calculus derivative chain rule

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, ..

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 differentiate a function of a function? Th..

Let f (x) be the real valued differentiable functio..

'Derivative of the product of two functions = first function x derivative of second function + second function x derivative of first function..

In this section, we derive the formulaIn this section, we derive the formula and use it to differentiate quotients of function..

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 r..

Conclusion - In this chapter we have learnt the application of derivatives to rate measure, also we have used the geometrical measurement of dy/dx to find the equations of the tangent and normal to a curve at any point on the curve, angle of intersection of the curve..

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 | (..

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 Functio..

The order of a differential equation is equal to the highest derivative in the equation. The single-quote indicates differentiation. So x ' is a first derivative, while x '' is a second derivative. x ' = 1/ x is first-order. x '' = - x is secon..