Calculus Examples

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

Step 1

Rewrite using the commutative property of multiplication.

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

Step 2

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

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Step 2.1

Move $x$ .

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

Step 2.2

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

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Step 2.2.1

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

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

Step 2.2.2

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

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

Step 2.3

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

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

Step 2.4

Combine the numerators over the common denominator.

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

Step 2.5

Add $2$ and $1$ .

$2 x^{\frac{3}{2}}$