Question

Math

Posted 5 months ago

```
$h(x)=\frac{\sin (x)}{3 x}$
How would you rewrite $h(x)$ so it can be differentiated using the product rule?
Assume $x \neq 0$.
```

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Answer from Sia

Posted 5 months ago

Solution by Steps

step 1

To differentiate $h(x) = \frac{\sin(x)}{3x}$ using the product rule, we first need to rewrite it as a product of two functions

step 2

We can express $h(x)$ as $h(x) = \frac{1}{3} \cdot \frac{\sin(x)}{x}$

step 3

Now, let $u(x) = \frac{1}{3}$ and $v(x) = \frac{\sin(x)}{x}$, so $h(x) = u(x) \cdot v(x)$

step 4

We can now apply the product rule, which states that $(u \cdot v)' = u' \cdot v + u \cdot v'$

Answer

To differentiate $h(x)$ using the product rule, rewrite it as $h(x) = \frac{1}{3} \cdot \frac{\sin(x)}{x}$ and then apply the product rule.

Key Concept

Product Rule for Differentiation

Explanation

The product rule allows us to differentiate products of two functions by taking the derivative of each function separately and combining the results as specified by the rule.

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