$$
h(x)=\frac{\sin (x)}{3 x}
$$

How would you rewrite $h(x)$ so it can be differentiated using the product rule?
Assume $x \neq 0$.

Question

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

Accepted Answer

∻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.⚹◊What is the derivative of the function $h(x)$ using the product rule?⍭ Generate me a similar question◊

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