Calculus Examples

$f (x) = 4 x$ , $f (x) = a x^{2}$

Step 1

Substitute $a x^{2}$ for $f (x)$ .

$a x^{2} = 4 x$

Step 2

Divide each term in $a x^{2} = 4 x$ by $x^{2}$ and simplify.

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Step 2.1

Divide each term in $a x^{2} = 4 x$ by $x^{2}$ .

$\frac{a x^{2}}{x^{2}} = \frac{4 x}{x^{2}}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $x^{2}$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{a x^{2}}{x^{2}} = \frac{4 x}{x^{2}}$

Step 2.2.1.2

Divide $a$ by $1$ .

$a = \frac{4 x}{x^{2}}$

$a = \frac{4 x}{x^{2}}$

$a = \frac{4 x}{x^{2}}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Cancel the common factor of $x$ and $x^{2}$ .

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Step 2.3.1.1

Factor $x$ out of $4 x$ .

$a = \frac{x \cdot 4}{x^{2}}$

Step 2.3.1.2

Cancel the common factors.

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Step 2.3.1.2.1

Factor $x$ out of $x^{2}$ .

$a = \frac{x \cdot 4}{x \cdot x}$

Step 2.3.1.2.2

Cancel the common factor.

$a = \frac{x \cdot 4}{x \cdot x}$

Step 2.3.1.2.3

Rewrite the expression.

$a = \frac{4}{x}$

$a = \frac{4}{x}$

$a = \frac{4}{x}$

$a = \frac{4}{x}$

$a = \frac{4}{x}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$