Calculus Examples

$x^{\frac{1}{2}} (\frac{1}{2} x^{- \frac{1}{2}})$

Step 1

Rewrite using the commutative property of multiplication.

$\frac{1}{2} x^{\frac{1}{2}} x^{- \frac{1}{2}}$

Step 2

Multiply $x^{\frac{1}{2}}$ by $x^{- \frac{1}{2}}$ by adding the exponents.

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Step 2.1

Move $x^{- \frac{1}{2}}$ .

$\frac{1}{2} (x^{- \frac{1}{2}} x^{\frac{1}{2}})$

Step 2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{1}{2} x^{- \frac{1}{2} + \frac{1}{2}}$

Step 2.3

Combine the numerators over the common denominator.

$\frac{1}{2} x^{\frac{- 1 + 1}{2}}$

Step 2.4

Add $- 1$ and $1$ .

$\frac{1}{2} x^{\frac{0}{2}}$

Step 2.5

Divide $0$ by $2$ .

$\frac{1}{2} x^{0}$

Step 3

Simplify $\frac{1}{2} x^{0}$ .

$\frac{1}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{2}$

Decimal Form:

$0.5$