Question

why do we do differentiation why x^2 becomes 2x.
What is the need of power(2) becomes a prefix coefficient of x(after differentiation)?

Answer 1

I'm not sure how detailed of an answer your teacher is looking for, but the product rule states that

f(x) = x^n

gives us a derivative of

f'(x) = n*x^(n-1)

so if we let n = 2, as per your example, we get

f'(x) = 2*x^1 = 2x

Answer 2

if your teacher is asking you WHY the product rule works, see the attached proof

Answer 3

okay Thank U :). I'll read and may ask you for doubts.

Answer 4

why did he wrote \[\frac{ f(x)-f(a) }{ x-a } \] a in the limit

Answer 5

what is the key behind the idea of limit. why to subtract f(a) from f(x) && dividing the numerator with x-a

Answer 6

definition of derivative

Answer 7

derivative of f(x) at x = a can be thought of as the rate of change from

f(a) to f(x)

Answer 8

so, we need to calculate how much f(x) changes between x and a, and divide by the difference between a and x

Answer 9

hope that makes sense

Answer 10

what actually mean a dervative. What is the need of it. (derivative-> are we doing any derivation out of it,:)

Answer 11

"derivative" is a function that describes the rate at which one variable changes in response to another variable

Answer 12

in order to prove why the derivative of

f(x) = x^n

is n*x^(n-1)

we need to calculate a general formula for f'(x) in terms of n and x

Answer 13

so we are "differentiating" f(x) WITHOUT using any of the standard differentiation formulas

Answer 14

okay, what i understood is in math, while dealing with graph eqns, we need to find the rate of change of the graph(is it sort of a behaviour of the graph, i'm curious:))

Answer 15

yeah, in general terms, derivative = rate of change

Answer 16

you learned in like algebra how to calculate slope, right? differentiating allows us to calculate the slope for any function at any location

Answer 17

if we pick a point on this function