Calculus Examples

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

Step 1

Apply the product rule to $3 x^{\frac{1}{2}}$ .

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

Step 2

Raise $3$ to the power of $2$ .

$9 {(x^{\frac{1}{2}})}^{2}$

Step 3

Multiply the exponents in ${(x^{\frac{1}{2}})}^{2}$ .

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Step 3.1

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

$9 x^{\frac{1}{2} \cdot 2}$

Step 3.2

Cancel the common factor of $2$ .

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Step 3.2.1

Cancel the common factor.

$9 x^{\frac{1}{2} \cdot 2}$

Step 3.2.2

Rewrite the expression.

$9 x^{1}$

Step 4

Simplify.

$9 x$