Calculus Examples

$y = \frac{4 x^{5}}{5}$

Step 1

Since $\frac{4}{5}$ is constant with respect to $x$ , the derivative of $\frac{4 x^{5}}{5}$ with respect to $x$ is $\frac{4}{5} \frac{d}{d x} [x^{5}]$ .

$\frac{4}{5} \frac{d}{d x} [x^{5}]$

Step 2

Differentiate using the Power Rule which states that $\frac{d}{d x} [x^{n}]$ is $n x^{n - 1}$ where $n = 5$ .

$\frac{4}{5} (5 x^{4})$

Step 3

Simplify terms.

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Step 3.1

Combine $5$ and $\frac{4}{5}$ .

$\frac{5 \cdot 4}{5} x^{4}$

Step 3.2

Multiply $5$ by $4$ .

$\frac{20}{5} x^{4}$

Step 3.3

Combine $\frac{20}{5}$ and $x^{4}$ .

$\frac{20 x^{4}}{5}$

Step 3.4

Cancel the common factor of $20$ and $5$ .

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Step 3.4.1

Factor $5$ out of $20 x^{4}$ .

$\frac{5 (4 x^{4})}{5}$

Step 3.4.2

Cancel the common factors.

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Step 3.4.2.1

Factor $5$ out of $5$ .

$\frac{5 (4 x^{4})}{5 (1)}$

Step 3.4.2.2

Cancel the common factor.

$\frac{5 (4 x^{4})}{5 \cdot 1}$

Step 3.4.2.3

Rewrite the expression.

$\frac{4 x^{4}}{1}$

Step 3.4.2.4

Divide $4 x^{4}$ by $1$ .

$4 x^{4}$