Calculus Examples

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

Step 1

Rewrite using the commutative property of multiplication.

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

Step 2

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

Tap for more steps...

Step 2.1

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

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

Step 2.2

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

Tap for more steps...

Step 2.2.1

Raise $x$ to the power of $1$ .

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

Step 2.2.2

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

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

Step 2.3

Write $1$ as a fraction with a common denominator.

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

Step 2.4

Combine the numerators over the common denominator.

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

Step 2.5

Add $- 1$ and $2$ .

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

Step 3

Combine $\frac{1}{2}$ and $x^{\frac{1}{2}}$ .

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