Calculus Examples

$f^{3} (g^{2} (x) h (x))$

Step 1

This derivative could not be completed using the chain rule. Mathway will use another method.

Step 2

Since $g^{2} x h (x)$ is constant with respect to $f$ , the derivative of $f^{3} g^{2} x h (x)$ with respect to $f$ is $g^{2} x h (x) \frac{d}{d f} [f^{3}]$ .

$g^{2} x h (x) \frac{d}{d f} [f^{3}]$

Step 3

Differentiate using the Power Rule which states that $\frac{d}{d f} [f^{n}]$ is $n f^{n - 1}$ where $n = 3$ .

$g^{2} x h (x) (3 f^{2})$

Step 4

Reorder.

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Step 4.1

Move $3$ to the left of $g^{2} x h (x)$ .

$3 \cdot (g^{2} x h (x)) f^{2}$

Step 4.2

Reorder the factors of $3 g^{2} x h (x) f^{2}$ .

$3 f^{2} g^{2} x h (x)$