Calculus Examples

$g (- 4) = \frac{13^{\frac{1}{2}}}{2 x^{\frac{1}{2}}}$

Step 1

Replace the variable $x$ with $- 4$ in the expression.

$g (- 4) = \frac{13^{\frac{1}{2}}}{2 {(- 4)}^{\frac{1}{2}}}$

Step 2

Simplify the result.

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Step 2.1

Simplify the denominator.

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Step 2.1.1

Rewrite $- 4$ as ${(2 i)}^{2}$ .

$g (- 4) = \frac{13^{\frac{1}{2}}}{2 {({(2 i)}^{2})}^{\frac{1}{2}}}$

Step 2.1.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$g (- 4) = \frac{13^{\frac{1}{2}}}{2 {(2 i)}^{2 (\frac{1}{2})}}$

Step 2.1.3

Cancel the common factor of $2$ .

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Step 2.1.3.1

Cancel the common factor.

$g (- 4) = \frac{13^{\frac{1}{2}}}{2 {(2 i)}^{2 (\frac{1}{2})}}$

Step 2.1.3.2

Rewrite the expression.

$g (- 4) = \frac{13^{\frac{1}{2}}}{2 (2 i)}$

Step 2.1.4

Simplify.

$g (- 4) = \frac{13^{\frac{1}{2}}}{2 \cdot (2 i)}$

Step 2.1.5

Multiply $2$ by $2$ .

$g (- 4) = \frac{13^{\frac{1}{2}}}{4 i}$

Step 2.2

Multiply the numerator and denominator of $\frac{13^{\frac{1}{2}}}{4 i}$ by the conjugate of $4 i$ to make the denominator real.

$g (- 4) = \frac{13^{\frac{1}{2}}}{4 i} \cdot \frac{i}{i}$

Step 2.3

Multiply.

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Step 2.3.1

Combine.

$g (- 4) = \frac{13^{\frac{1}{2}} i}{4 i i}$

Step 2.3.2

Reorder factors in $13^{\frac{1}{2}} i$ .

$g (- 4) = \frac{i \cdot 13^{\frac{1}{2}}}{4 i i}$

Step 2.3.3

Simplify the denominator.

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Step 2.3.3.1

Add parentheses.

$g (- 4) = \frac{i \cdot 13^{\frac{1}{2}}}{4 (i i)}$

Step 2.3.3.2

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

$g (- 4) = \frac{i \cdot 13^{\frac{1}{2}}}{4 (i i)}$

Step 2.3.3.3

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

$g (- 4) = \frac{i \cdot 13^{\frac{1}{2}}}{4 (i i)}$

Step 2.3.3.4

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

$g (- 4) = \frac{i \cdot 13^{\frac{1}{2}}}{4 i^{1 + 1}}$

Step 2.3.3.5

Add $1$ and $1$ .

$g (- 4) = \frac{i \cdot 13^{\frac{1}{2}}}{4 i^{2}}$

Step 2.3.3.6

Rewrite $i^{2}$ as $- 1$ .

$g (- 4) = \frac{i \cdot 13^{\frac{1}{2}}}{4 \cdot - 1}$

Step 2.4

Multiply $4$ by $- 1$ .

$g (- 4) = \frac{i \cdot 13^{\frac{1}{2}}}{- 4}$

Step 2.5

Move the negative in front of the fraction.

$g (- 4) = - \frac{i \cdot 13^{\frac{1}{2}}}{4}$

Step 2.6

The final answer is $- \frac{i \cdot 13^{\frac{1}{2}}}{4}$ .

$- \frac{i \cdot 13^{\frac{1}{2}}}{4}$

Step 3