What the differentiation and anti-differentiation formula?

Answer 1

There is no single formula for differentiation and anti-differentiation.

The deriviative of a function y = f(x) is the limit of delta y over delta x as delta x approaches zero.

OR:

If f(x)=axn,

f'(x)=(an)xn-1

The deriviative of 2x3 would be 6x2.

The anti-deriviative of a function is the reverse operation, i.e. the function is the deriviative of the anti-deriviative.

Anti differentiation introduction:

Anti differentiation is also called as integration process. It gives the reverse value of the differentiation equation. Anti differentiation is also called as anti derivative of the function. In this anti differentiation, f(x) is anti derivative of the function F(x). Anti differentiation is used for finding the area of the region under the certain curve. Anti differentiation symbol is denoted as ∫.

General formula for anti differentiation:

∫ xn dx = [xn + 1 / (n + 1)]+ c

∫ k dx = k ∫ dx

∫ udv = uv - ∫ v du

∫ (w + y) dx = ∫ w dx + ∫ y dx

anti-differentiation