Question

can anyone help me to understand differntiation

Answer 1

Sure, which part?

Answer 2

begin with "limit".. differentiation won't be difficult... a bit of practice will do.. but then if there are any particular problems u can always feel free to ask it..
P.S. better if its posted on mathematics group.. :p

Answer 3

Differentiation can be viewed simply as an effective tool to analyze any function. From the word differentiate, we can see that we're trying to simplify a complex function. It is in fact true because a function would often look "leaner" once differentiated. You need differentiation because functions like \[y=x^{2}\] have changing slopes, which means that they increase or decrease at different rate at any different given point on the x-axis. Using differentiation, you can find out the general formula to find the slope. For example, the general formula to find slope of the function y=x^2 would be y=2x. Then, you can plug in the x-value to find out the slope of the function at that x coordinate. Another way to define derivative, or the slope, would be rate of change. Rate of change tells you how quickly a function increases or decreases. The physical meaning of this rate may be "the temperature is rising very sharply, the speed of the red car is very small, the water is suddenly pouring forth from the faucet." In the first two cases, we can tell how the nature of some action changes in a period of time. In the case of the water, we can use derivative to find out how the nature of some action behaves at one instance. Other applications of differentiation include approximation using differential equation or linearization, as well as finding the gradient(derivative of a 3 d fucntion), which I will not specify.

My word is advice for learning differentiation is to understand it graphically at first, and then commit yourself to memorize the differentiation results of different basic functions by practicing long and difficult differentiation problems. After you practice many differentiation problems, you should find differentiation to be a tedious and mechanical process which can be easily done most of the time.