Differentiation techniques

Differentiation techniques

In this section we will discuss about different techniques to obtain the derivatives of the given functions.

1. Some standard results [formulae]

2. General rules for differentiation

3. Derivative of implicit functions

For the implicit function f(x,y) = 0, differentiate each term with respect to x treating y as a function of x and then collect the terms of dy/dx together on left hand side and remaining terms on the right hand side and then find dy/dx.

4. Logarithmic differentiation

Some times, the function whose derivative is required involves products, quotients, and powers. For such cases, differentiation can be carried out more conveniently if we take logarithms and simplify before differentiation.

5. Differentiation of parametric functions

If the variables x and y are functions of another variable namely t, then the functions are called a parametric functions. The variable t is called the parameter of the function.

6. Differentiation of a function with respect to another function

Let u = f(x) and v = g(x) be two functions of x. The derivative of f(x) with respect to g(x) is given by the formula,

7. Successive differentiation

The process of differentiating the same function again and again is called successive differentiation.