what are the rules of differentiation and intergration in mathematics?

Answer 1

For all the rules of differentiation and integration, check sources

Answer 2

thats a bit general!

without stating the fundamental theorem of calculus, basic rules are:

1) differentiation and integration are the reverse of each other.
2) chain rule, product rule quotient rule are methods of differentiating.
3) substitution, integration by parts, numerical method approximation are methods of integrating.

There are no general rules for differentiating or integrating an arbitrary function.

The definition of differentation is,

lim x->oo [ f(x+h) - f(x) ]/ h = df/dx

for a function of one variable. Alot more could be written but it could go on 4 a while.....

Answer 3

Lol there are just a few but in general...they are derived from f'(x) = (f(x+h) f(x))/h

for deriving

if,
f(x) = x^k
f'(x)(first derivitive) = kx^(k-1)
so
f(x) = x^3
f'(x) = 3x^2

for integrating

if
f'(x) = x^k
F(x)= x^(k+1)/(k+1)+c (just a constant)

so,
f'(x)= x^2
F(x) = (x^3)/3 + c

Just a few others are
The chain rule (for deriving)
f(x)=a(kx-3)^z
f'(x)= ak(kx-3)^(z-1)

The production rule (also for deriving) when u have 2 terms that are multiplied

f(x) = uv
f'(x) = u'v+ v'u

so,
f(x) = x^2 * 3(2x-3)^3
f'(x)= 2x*3(2x-3)^3 - 6(2x-3)^2 * x^2

There are many other rules for intergration and deriving but the ones show are the basics

Answer 4

I'm not going to bother.
Check the wikipedia entries for chain rule, product rule and quotient rule.
Try Gilbert Strang's Calculus if you need a good self-study resource.

Answer 5

when differentiating, the indicie is multiplied by the number infront of the pronumeral, and then you take 1 away from the indicie. For example:
y=6z ^ 4
differentiated=6x4z^(4-1)
=24x^3

Answer 6

the rules 1. define differentiation, 2 define Intergration.

The standard def of differentiation is f(x)=y, LIM(h->0) [f(x + h)-f(x)]/h == f'(x) ==[( y+e)-y]/[(x+h)-x] == y' thus e == dy h== dx { d standind for delta}

You can then use this def to define anti-differintation ie Y'= y to Y = int* y .