Calculus Examples

$f (x) = x^{3} + 3$ , $g (x) = \sqrt[3]{x}$ , $(g \cdot f) (x)$

Step 1

Evaluate $g \cdot f$ .

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Step 1.1

Replace the function designators in $g \cdot f$ with the actual functions.

$(\sqrt[3]{x}) \cdot (x^{3} + 3)$

Step 1.2

Apply the distributive property.

$\sqrt[3]{x} x^{3} + \sqrt[3]{x} \cdot 3$

Step 1.3

Move $3$ to the left of $\sqrt[3]{x}$ .

$\sqrt[3]{x} x^{3} + 3 \sqrt[3]{x}$

Step 2

Evaluate $g \cdot f$ at $x$ .

$\sqrt[3]{x} {(x)}^{3} + 3 \sqrt[3]{x}$

Step 3

Simplify $\sqrt[3]{x} {(x)}^{3} + 3 \sqrt[3]{x}$ .

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Step 3.1

Remove parentheses.

$(\sqrt[3]{x} {(x)}^{3} + 3 \sqrt[3]{x})$

Step 3.2

Remove parentheses.

$\sqrt[3]{x} {(x)}^{3} + 3 \sqrt[3]{x}$

Step 3.3

Remove parentheses.

$\sqrt[3]{x} x^{3} + 3 \sqrt[3]{x}$