Differentiation: Overview, Questions, Preparation

The method of finding the derivative of any function is known as differentiation. 

The derivative of f is denoted by f’(x) or d/dx f(x). f’(x) can also be written as ‘differentiate with respect to x.’

The derivative of f at c is defined by:

Some Basic Results and Rules of Differentiation

5. Derivatives of trigonometric functions

6. Derivative of the algebraic sum of two functions

If y = u+v and u and v are the functions of x, 

7. Product rule
If y = uv and u and v are functions of x, 

8. Quotient rule
If y = u/v and u and v are the functions of x, 

9. Chain rule
If y = f[g(x)] and u = g(x) then y = f(u) and

10. Differentiation of e^x and a^x

The introduction of this topic has already been given in Class 11. In Class 12, this chapter carries 10-15 marks. This topic is a very important part of your board's syllabus. Apart from that, if you are thinking of pursuing engineering, then your differentiation should be very strong.

1. Differentiate the function with respect to x: sin(x²+5)

Solution.

Let y= sin(x²+5)

Differentiating both sides with respect to x

2. Find dy/dx of: 2x + 3y = sin x

Solution.

On differentiating with respect to x,

3. Find dy/dx of: xy + y²= tan x + y

Solution.

On differentiating with respect to x,

Q: Is every continuous function derivable?

Q: What is the differentiation of 0?

Q: What is the differentiation of log_ex?

Q: Is every derivable function continuous?

Q: Is the differentiation of inverse trigonometric functions possible?