Calculus Examples

$f (9) = (\sqrt{x} + 4 x) (x^{\frac{3}{2}} - x)$

Step 1

Replace the variable $x$ with $9$ in the expression.

$f (9) = (\sqrt{9} + 4 (9)) ({(9)}^{\frac{3}{2}} - (9))$

Step 2

Simplify the result.

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Step 2.1

Remove parentheses.

$f (9) = (\sqrt{9} + 4 (9)) ({(9)}^{\frac{3}{2}} - (9))$

Step 2.2

Simplify each term.

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Step 2.2.1

Rewrite $9$ as $3^{2}$ .

$f (9) = (\sqrt{3^{2}} + 4 (9)) ({(9)}^{\frac{3}{2}} - (9))$

Step 2.2.2

Pull terms out from under the radical, assuming positive real numbers.

$f (9) = (3 + 4 (9)) ({(9)}^{\frac{3}{2}} - (9))$

Step 2.2.3

Multiply $4$ by $9$ .

$f (9) = (3 + 36) ({(9)}^{\frac{3}{2}} - (9))$

Step 2.3

Add $3$ and $36$ .

$f (9) = 39 ({(9)}^{\frac{3}{2}} - (9))$

Step 2.4

Simplify each term.

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Step 2.4.1

Rewrite $9$ as $3^{2}$ .

$f (9) = 39 ({(3^{2})}^{\frac{3}{2}} - (9))$

Step 2.4.2

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

$f (9) = 39 (3^{2 (\frac{3}{2})} - (9))$

Step 2.4.3

Cancel the common factor of $2$ .

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Step 2.4.3.1

Cancel the common factor.

$f (9) = 39 (3^{2 (\frac{3}{2})} - (9))$

Step 2.4.3.2

Rewrite the expression.

$f (9) = 39 (3^{3} - (9))$

Step 2.4.4

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

$f (9) = 39 (27 - (9))$

Step 2.4.5

Multiply $- 1$ by $9$ .

$f (9) = 39 (27 - 9)$

Step 2.5

Simplify the expression.

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Step 2.5.1

Subtract $9$ from $27$ .

$f (9) = 39 \cdot 18$

Step 2.5.2

Multiply $39$ by $18$ .

$f (9) = 702$

Step 2.6

The final answer is $702$ .

$702$

Step 3