The reverse process of the derivative or a differential is called **antidifferentiation**.

If \(F(x) = 2x^3 \), then \(F'(x) = 6x^2 \)

Thus, we can call \(f(x) = 2x^3 \) the **antiderivative **of \(F'(x) = 6x^2 \)

Let's find the anitderivative \(F(x) \) such that \(f(x) = x^3\)

We know the power rule for the derivative decreases the power by 1,

\(\therefore \) \(F(x) \) must have the power \(x^4 \) and \[\frac{d}{dx}x^4 = 4x^3 \]

Now let's find the coefficient \( a \) of \(F(x) \) such that \(F'(x) = x^3 \)

If \(a = \frac{1}{4} \) then \(F(x) = \frac{x^4}{4} \) and \(F'(x) = x^3 = f(x) \)

\[\frac{d}{dx}sinx = cosx, \]\(cosx \) is the antiderivative of \(sinx \),

and \(e^x \) is the antiderivative of \(e^x \)