Calculus Examples

$x (\frac{- 744}{{(0.3 x^{2} + 8)}^{2}}) (\frac{1240}{0.3 x^{2} + 8})$

Step 1

Factor $0.1$ out of $0.3 x^{2} + 8$ .

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Step 1.1

Factor $0.1$ out of $0.3 x^{2}$ .

$x (\frac{- 744}{{(0.3 x^{2} + 8)}^{2}}) \cdot \frac{1240}{0.1 (3 x^{2}) + 8}$

Step 1.2

Factor $0.1$ out of $8$ .

$x (\frac{- 744}{{(0.3 x^{2} + 8)}^{2}}) \cdot \frac{1240}{0.1 (3 x^{2}) + 0.1 (80)}$

Step 1.3

Factor $0.1$ out of $0.1 (3 x^{2}) + 0.1 (80)$ .

$x (\frac{- 744}{{(0.3 x^{2} + 8)}^{2}}) \cdot \frac{1240}{0.1 (3 x^{2} + 80)}$

Step 2

Simplify the denominator.

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Step 2.1

Factor $0.1$ out of $0.3 x^{2} + 8$ .

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Step 2.1.1

Factor $0.1$ out of $0.3 x^{2}$ .

$x \frac{- 744}{{(0.1 (3 x^{2}) + 8)}^{2}} \cdot \frac{1240}{0.1 (3 x^{2} + 80)}$

Step 2.1.2

Factor $0.1$ out of $8$ .

$x \frac{- 744}{{(0.1 (3 x^{2}) + 0.1 (80))}^{2}} \cdot \frac{1240}{0.1 (3 x^{2} + 80)}$

Step 2.1.3

Factor $0.1$ out of $0.1 (3 x^{2}) + 0.1 (80)$ .

$x \frac{- 744}{{(0.1 (3 x^{2} + 80))}^{2}} \cdot \frac{1240}{0.1 (3 x^{2} + 80)}$

Step 2.2

Apply the product rule to $0.1 (3 x^{2} + 80)$ .

$x \frac{- 744}{{0.1}^{2} {(3 x^{2} + 80)}^{2}} \cdot \frac{1240}{0.1 (3 x^{2} + 80)}$

Step 2.3

Raise $0.1$ to the power of $2$ .

$x \frac{- 744}{0.01 {(3 x^{2} + 80)}^{2}} \cdot \frac{1240}{0.1 (3 x^{2} + 80)}$

Step 3

Simplify terms.

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Step 3.1

Move the negative in front of the fraction.

$x (- \frac{744}{0.01 {(3 x^{2} + 80)}^{2}}) \cdot \frac{1240}{0.1 (3 x^{2} + 80)}$

Step 3.2

Cancel the common factor of $0.1$ .

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Step 3.2.1

Factor $0.1$ out of $x (- \frac{744}{0.01 {(3 x^{2} + 80)}^{2}})$ .

$0.1 (x (- 10 \frac{744}{0.01 {(3 x^{2} + 80)}^{2}})) \cdot \frac{1240}{0.1 (3 x^{2} + 80)}$

Step 3.2.2

Cancel the common factor.

$0.1 (x (- 10 \frac{744}{0.01 {(3 x^{2} + 80)}^{2}})) \cdot \frac{1240}{0.1 (3 x^{2} + 80)}$

Step 3.2.3

Rewrite the expression.

$x (- 10 \frac{744}{0.01 {(3 x^{2} + 80)}^{2}}) \cdot \frac{1240}{3 x^{2} + 80}$

Step 3.3

Combine $- 10$ and $\frac{744}{0.01 {(3 x^{2} + 80)}^{2}}$ .

$x \frac{- 10 \cdot 744}{0.01 {(3 x^{2} + 80)}^{2}} \cdot \frac{1240}{3 x^{2} + 80}$

Step 3.4

Multiply $- 10$ by $744$ .

$x \frac{- 7440}{0.01 {(3 x^{2} + 80)}^{2}} \cdot \frac{1240}{3 x^{2} + 80}$

Step 3.5

Combine $x$ and $\frac{- 7440}{0.01 {(3 x^{2} + 80)}^{2}}$ .

$\frac{x \cdot - 7440}{0.01 {(3 x^{2} + 80)}^{2}} \cdot \frac{1240}{3 x^{2} + 80}$

Step 3.6

Multiply $\frac{x \cdot - 7440}{0.01 {(3 x^{2} + 80)}^{2}}$ by $\frac{1240}{3 x^{2} + 80}$ .

$\frac{x \cdot - 7440 \cdot 1240}{0.01 {(3 x^{2} + 80)}^{2} (3 x^{2} + 80)}$

Step 3.7

Multiply $1240$ by $- 7440$ .

$\frac{x \cdot - 9225600}{0.01 {(3 x^{2} + 80)}^{2} (3 x^{2} + 80)}$

Step 4

Raise $3 x^{2} + 80$ to the power of $1$ .

$\frac{x \cdot - 9225600}{0.01 ({(3 x^{2} + 80)}^{1} {(3 x^{2} + 80)}^{2})}$

Step 5

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

$\frac{x \cdot - 9225600}{0.01 {(3 x^{2} + 80)}^{1 + 2}}$

Step 6

Simplify the expression.

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Step 6.1

Add $1$ and $2$ .

$\frac{x \cdot - 9225600}{0.01 {(3 x^{2} + 80)}^{3}}$

Step 6.2

Move $- 9225600$ to the left of $x$ .

$\frac{- 9225600 \cdot x}{0.01 {(3 x^{2} + 80)}^{3}}$

Step 6.3

Move the negative in front of the fraction.

$- \frac{9225600 \cdot x}{0.01 {(3 x^{2} + 80)}^{3}}$

Step 7

Factor $9225600$ out of $9225600 \cdot x$ .

$- \frac{9225600 (x)}{0.01 {(3 x^{2} + 80)}^{3}}$

Step 8

Factor $0.01$ out of $0.01 {(3 x^{2} + 80)}^{3}$ .

$- \frac{9225600 (x)}{0.01 ({(3 x^{2} + 80)}^{3})}$

Step 9

Separate fractions.

$- (\frac{9225600}{0.01} \cdot \frac{x}{{(3 x^{2} + 80)}^{3}})$

Step 10

Divide $9225600$ by $0.01$ .

$- (922560000 \frac{x}{{(3 x^{2} + 80)}^{3}})$

Step 11

Combine $922560000$ and $\frac{x}{{(3 x^{2} + 80)}^{3}}$ .

$- \frac{922560000 x}{{(3 x^{2} + 80)}^{3}}$