Calculus Examples

$f^{2} (x)$

Step 1

Since $x$ is constant with respect to $f$ , the derivative of $f^{2} x$ with respect to $f$ is $x \frac{d}{d f} [f^{2}]$ .

$x \frac{d}{d f} [f^{2}]$

Step 2

Differentiate using the Power Rule which states that $\frac{d}{d f} [f^{n}]$ is $n f^{n - 1}$ where $n = 2$ .

$x (2 f)$

Step 3

Reorder.

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Step 3.1

Move $2$ to the left of $x$ .

$2 \cdot x f$

Step 3.2

Reorder the factors of $2 x f$ .

$2 f x$