Calculus Examples

$f (\frac{1}{5}) = 15 x^{4} - 4 x^{3}$

Step 1

Replace the variable $x$ with $\frac{1}{5}$ in the expression.

$f (\frac{1}{5}) = 15 {(\frac{1}{5})}^{4} - 4 {(\frac{1}{5})}^{3}$

Step 2

Simplify the result.

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the product rule to $\frac{1}{5}$ .

$f (\frac{1}{5}) = 15 (\frac{1^{4}}{5^{4}}) - 4 {(\frac{1}{5})}^{3}$

Step 2.1.2

One to any power is one.

$f (\frac{1}{5}) = 15 (\frac{1}{5^{4}}) - 4 {(\frac{1}{5})}^{3}$

Step 2.1.3

Raise $5$ to the power of $4$ .

$f (\frac{1}{5}) = 15 (\frac{1}{625}) - 4 {(\frac{1}{5})}^{3}$

Step 2.1.4

Cancel the common factor of $5$ .

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Step 2.1.4.1

Factor $5$ out of $15$ .

$f (\frac{1}{5}) = 5 (3) (\frac{1}{625}) - 4 {(\frac{1}{5})}^{3}$

Step 2.1.4.2

Factor $5$ out of $625$ .

$f (\frac{1}{5}) = 5 \cdot (3 (\frac{1}{5 \cdot 125})) - 4 {(\frac{1}{5})}^{3}$

Step 2.1.4.3

Cancel the common factor.

$f (\frac{1}{5}) = 5 \cdot (3 (\frac{1}{5 \cdot 125})) - 4 {(\frac{1}{5})}^{3}$

Step 2.1.4.4

Rewrite the expression.

$f (\frac{1}{5}) = 3 (\frac{1}{125}) - 4 {(\frac{1}{5})}^{3}$

Step 2.1.5

Combine $3$ and $\frac{1}{125}$ .

$f (\frac{1}{5}) = \frac{3}{125} - 4 {(\frac{1}{5})}^{3}$

Step 2.1.6

Apply the product rule to $\frac{1}{5}$ .

$f (\frac{1}{5}) = \frac{3}{125} - 4 \frac{1^{3}}{5^{3}}$

Step 2.1.7

One to any power is one.

$f (\frac{1}{5}) = \frac{3}{125} - 4 \frac{1}{5^{3}}$

Step 2.1.8

Raise $5$ to the power of $3$ .

$f (\frac{1}{5}) = \frac{3}{125} - 4 (\frac{1}{125})$

Step 2.1.9

Combine $- 4$ and $\frac{1}{125}$ .

$f (\frac{1}{5}) = \frac{3}{125} + \frac{- 4}{125}$

Step 2.1.10

Move the negative in front of the fraction.

$f (\frac{1}{5}) = \frac{3}{125} - \frac{4}{125}$

Step 2.2

Combine fractions.

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Step 2.2.1

Combine the numerators over the common denominator.

$f (\frac{1}{5}) = \frac{3 - 4}{125}$

Step 2.2.2

Simplify the expression.

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Step 2.2.2.1

Subtract $4$ from $3$ .

$f (\frac{1}{5}) = \frac{- 1}{125}$

Step 2.2.2.2

Move the negative in front of the fraction.

$f (\frac{1}{5}) = - \frac{1}{125}$

Step 2.3

The final answer is $- \frac{1}{125}$ .

$- \frac{1}{125}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$- \frac{1}{125}$

Decimal Form:

$- 0.008$

Step 4