An equation involving an independent variable (variables), dependent variable and derivative or derivatives of the dependent variable with respect to the independent variable (variables) is called a differential equation.
It is an equation involving unknown functions and their derivatives w.r.t. one or more independent variables.
CBSE Class 11 - Mathematics - Limits and Derivatives Part-11
Working rule for finding the derivative of implicit functions
First method:
Differentiate every term of f (x, y) = 0 with respect to x.
CBSE Class 11 - Mathematics - Limits and Derivatives Part-10
You have learnt theorems of differentiation part-9. Let us proceed further. Here is a list of differentiation of some standard functions:
CBSE Class 11 - Mathematics - Limits and Derivatives Part-9
You have learnt about finding derivatives using the first principle in part-7 and part-8. Let us proceed further. Here is a summary of theorems on differentiation.
Derivatives Using First Principle
Q1: What is the derivative of a function at a point?
Answer: Let y = f(x) is a continuous function. It means the value of y changes as the value of x changes.
At x = a, is a point in its domain of definittion. The derivative of f at a is defines as:
