Calculus Examples

$m x^{m - 1}$

Step 1

Since $m$ is constant with respect to $x$ , the derivative of $m x^{m - 1}$ with respect to $x$ is $m \frac{d}{d x} [x^{m - 1}]$ .

$m \frac{d}{d x} [x^{m - 1}]$

Step 2

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

$m ((m - 1) x^{m - 1 - 1})$

Step 3

Simplify the expression.

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Step 3.1

Subtract $1$ from $- 1$ .

$m ((m - 1) x^{m - 2})$

Step 3.2

Reorder the factors of $m ((m - 1) x^{m - 2})$ .

$x^{m - 2} m (m - 1)$