Calculus Examples

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

Step 1

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

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Step 1.1

Move $x$ .

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

Step 1.2

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

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Step 1.2.1

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

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

Step 1.2.2

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

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

Step 1.3

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

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

Step 1.4

Combine the numerators over the common denominator.

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

Step 1.5

Subtract $1$ from $2$ .

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

Step 2

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

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