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Question
Math
Posted 10 months ago
h(x)=sin(x)3x
h(x)=\frac{\sin (x)}{3 x}


How would you rewrite h(x)h(x) so it can be differentiated using the product rule?
Assume x0x \neq 0.
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Answer from Sia
Posted 10 months ago
Solution by Steps
step 1
To differentiate h(x)=sin(x)3xh(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)h(x) as h(x)=13sin(x)xh(x) = \frac{1}{3} \cdot \frac{\sin(x)}{x}
step 3
Now, let u(x)=13u(x) = \frac{1}{3} and v(x)=sin(x)xv(x) = \frac{\sin(x)}{x}, so h(x)=u(x)v(x)h(x) = u(x) \cdot v(x)
step 4
We can now apply the product rule, which states that (uv)=uv+uv(u \cdot v)' = u' \cdot v + u \cdot v'
Answer
To differentiate h(x)h(x) using the product rule, rewrite it as h(x)=13sin(x)xh(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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