Calculus Examples

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

Step 1

Move $x^{\frac{1}{2}}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

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

Step 2

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

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Step 2.1

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

$3 (x^{- \frac{1}{2}} x) \sqrt{3}$

Step 2.2

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

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Step 2.2.1

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

$3 (x^{- \frac{1}{2}} x^{1}) \sqrt{3}$

Step 2.2.2

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

$3 x^{- \frac{1}{2} + 1} \sqrt{3}$

Step 2.3

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

$3 x^{- \frac{1}{2} + \frac{2}{2}} \sqrt{3}$

Step 2.4

Combine the numerators over the common denominator.

$3 x^{\frac{- 1 + 2}{2}} \sqrt{3}$

Step 2.5

Add $- 1$ and $2$ .

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