Calculus Examples

$f (- 1) f (x) x^{3} - 5 x - 1$

Step 1

Multiply $f$ by $f$ by adding the exponents.

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Step 1.1

Move $f$ .

$f \cdot f \cdot - 1 x \cdot x^{3} - 5 x - 1$

Step 1.2

Multiply $f$ by $f$ .

$f^{2} \cdot - 1 x \cdot x^{3} - 5 x - 1$

$f^{2} \cdot - 1 x \cdot x^{3} - 5 x - 1$

Step 2

Multiply $x$ by $x^{3}$ by adding the exponents.

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Step 2.1

Move $x^{3}$ .

$f^{2} \cdot - 1 (x^{3} x) - 5 x - 1$

Step 2.2

Multiply $x^{3}$ by $x$ .

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Step 2.2.1

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

$f^{2} \cdot - 1 (x^{3} x^{1}) - 5 x - 1$

Step 2.2.2

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

$f^{2} \cdot - 1 x^{3 + 1} - 5 x - 1$

$f^{2} \cdot - 1 x^{3 + 1} - 5 x - 1$

Step 2.3

Add $3$ and $1$ .

$f^{2} \cdot - 1 x^{4} - 5 x - 1$

$f^{2} \cdot - 1 x^{4} - 5 x - 1$

Step 3

Move $- 1$ to the left of $f^{2}$ .

$- 1 \cdot f^{2} x^{4} - 5 x - 1$

Step 4

Rewrite $- 1 f^{2}$ as $- f^{2}$ .

$- f^{2} x^{4} - 5 x - 1$

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