1. Differentiation is the process of finding the derivative of a function, denoted as f'(x) or dy/dx, to determine how the value of the function changes as the input variable changes. 2. Some basic derivative formulas are that the derivative of a constant is 0, the derivative of ax is a, and the derivative of the sum of two functions u and v is the sum of their individual derivatives. 3. As examples, the derivative of x^2 is 2x, and the derivative of 2x + 4 is 2.

1. Differentiation
By Sanjna

2. Differentiation
1-The derivative of f is denoted by f ′ (x) or
if y = f (x) then derivative is dy/dx or y’
2-The process of finding
derivative of a function is called differentiation. We also
use the phrase differentiate f (x) with respect to x to
mean find f ′(x).

3. Formulae
Basic set of derivatives
-Derivative of constants like 1,2 .... is always 0.
- d(ax)/dx = a where a is a constant.

4. Result :
1. d(u+v)/dx= du/dx + dv/dx
2. d(u-v)/dx = du/dx - dv/dx

5. Example 1
Differentiate function with respect to x:
f(x)=x^2
When f(x) = x^n then f’(x)=nx^(n-1)
Here n= 2
f’(x)= 2.x^(2-1)
=2x
f’(x)=2x

6. Example 2
Differentiate function with respect to x:
f(x)=2x+4
Here we will use the addition result of derivatives.
f’(x)= d(2x+4 )/x
=d(2x)/dx + d(4)/dx
= 2 + 0 ............[ check formula slide for ax
and constant.]
f’(x)=2

7. Assessment
Differentiate function with respect to x:
f(x)=3x^2+7

8. Thanks
Sanjna
Phone:7498524452
Email:sanjnad7@gmail.com
Skype:sanjna.balaji