Calculus Examples

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

Step 1

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

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Step 1.1

Move $x^{2}$ .

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

Step 1.2

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

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

Step 1.3

To write $2$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Step 1.4

Combine $2$ and $\frac{2}{2}$ .

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

Step 1.5

Combine the numerators over the common denominator.

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

Step 1.6

Simplify the numerator.

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Step 1.6.1

Multiply $2$ by $2$ .

$\frac{1}{2} x^{\frac{4 - 1}{2}}$

Step 1.6.2

Subtract $1$ from $4$ .

$\frac{1}{2} x^{\frac{3}{2}}$

Step 2

Combine $\frac{1}{2}$ and $x^{\frac{3}{2}}$ .

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