Calculus Examples

$y = x^{9} f (x)$

Step 1

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

Step 2

Raise $x$ to the power of $1$ .

$\frac{d}{d x} [f (x^{9} x^{1})]$

Step 3

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{d}{d x} [f x^{9 + 1}]$

Step 4

Add $9$ and $1$ .

$\frac{d}{d x} [f x^{10}]$

Step 5

Since $f$ is constant with respect to $x$ , the derivative of $f x^{10}$ with respect to $x$ is $f \frac{d}{d x} [x^{10}]$ .

$f \frac{d}{d x} [x^{10}]$

Step 6

Differentiate using the Power Rule which states that $\frac{d}{d x} [x^{n}]$ is $n x^{n - 1}$ where $n = 10$ .

$f (10 x^{9})$

Step 7

Reorder.

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Step 7.1

Move $10$ to the left of $f$ .

$10 \cdot f x^{9}$

Step 7.2

Reorder the factors of $10 f x^{9}$ .

$10 x^{9} f$