Calculus Examples

$x^{2} (- \frac{x}{4} + \frac{2700}{x})$

Step 1

Simplify terms.

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Step 1.1

Apply the distributive property.

$x^{2} (- \frac{x}{4}) + x^{2} \frac{2700}{x}$

Step 1.2

Rewrite using the commutative property of multiplication.

$- x^{2} \frac{x}{4} + x^{2} \frac{2700}{x}$

Step 1.3

Cancel the common factor of $x$ .

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Step 1.3.1

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

$- x^{2} \frac{x}{4} + x \cdot x \frac{2700}{x}$

Step 1.3.2

Cancel the common factor.

$- x^{2} \frac{x}{4} + x \cdot x \frac{2700}{x}$

Step 1.3.3

Rewrite the expression.

$- x^{2} \frac{x}{4} + x \cdot 2700$

Step 2

Simplify each term.

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Step 2.1

Multiply $- x^{2} \frac{x}{4}$ .

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Step 2.1.1

Combine $\frac{x}{4}$ and $x^{2}$ .

$- \frac{x \cdot x^{2}}{4} + x \cdot 2700$

Step 2.1.2

Multiply $x$ by $x^{2}$ by adding the exponents.

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Step 2.1.2.1

Multiply $x$ by $x^{2}$ .

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Step 2.1.2.1.1

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

$- \frac{x^{1} x^{2}}{4} + x \cdot 2700$

Step 2.1.2.1.2

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

$- \frac{x^{1 + 2}}{4} + x \cdot 2700$

Step 2.1.2.2

Add $1$ and $2$ .

$- \frac{x^{3}}{4} + x \cdot 2700$

Step 2.2

Move $2700$ to the left of $x$ .

$- \frac{x^{3}}{4} + 2700 x$