differentiate x^2 and integrate x

Let's differentiate:

\frac{d}{d x} (x^{2})

ⓘ The derivative of

x^{n}

n x^{n - 1}

\frac{d}{d x} (x^{2})

2 x

▶Derivative:

2 x

Let's integrate:

\int x d x

ⓘ For constant

n

with

n \neq -1

\frac{x^{n + 1}}{n + 1}

is an antiderivative of

x^{n}

\int x d x

\frac{x^{2}}{2}

\frac{x^{2}}{2}

▶Indefinite integrals are defined up to an additive constant C, so this yields:

\frac{x^{2}}{2} + C

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