Calculus Examples

$y = 3 x^{5 p}$

Step 1

Since $3$ is constant with respect to $x$ , the derivative of $3 x^{5 p}$ with respect to $x$ is $3 \frac{d}{d x} [x^{5 p}]$ .

$3 \frac{d}{d x} [x^{5 p}]$

Step 2

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

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

Step 3

Multiply $5$ by $3$ .

$15 (p x^{5 p - 1})$

Step 4

Simplify.

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Step 4.1

Reorder the factors of $15 p x^{5 p - 1}$ .

$15 x^{5 p - 1} p$

Step 4.2

Reorder factors in $15 x^{5 p - 1} p$ .

$15 p x^{5 p - 1}$