The derivative of sin(x)/x^2e^x?

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In summary, to find the derivative of y=(sinx)/(x^2e^x), you can use the quotient rule, but when differentiating the denominator, you will need to use the product rule within the quotient rule. This will result in a more complex differentiation process.
  • #1
dylanhouse
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I need to find the derivative of y=(sinx)/(x^2e^x)?

I tried using the product rule on the denominator and then I assume I need to use the quotient rule. But I'm not sure if I use the quotient rule with the derivative I found for the denominator or? I'm confused :$
 
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  • #2
dylanhouse said:
I need to find the derivative of y=(sinx)/(x^2e^x)?

I tried using the product rule on the denominator and then I assume I need to use the quotient rule. But I'm not sure if I use the quotient rule with the derivative I found for the denominator or? I'm confused :$

You have the idea. You start differentiating with the quotient rule. In the process of doing that, at the part where you have to differentiate the denominator, right there use the product rule to differentiate the denominator, then continue. So you use the product rule in the middle of doing the quotient rule.
 

1. What is the derivative of sin(x)/x^2e^x?

The derivative of sin(x)/x^2e^x is (x^2e^x(cos(x))-2sin(x)e^x-x^2e^x(sin(x)))/x^4.

2. How do you simplify the derivative of sin(x)/x^2e^x?

To simplify the derivative, you can use the quotient rule and chain rule to expand the terms and then combine like terms to get the final simplified expression.

3. Can you provide an example of how to find the derivative of sin(x)/x^2e^x?

For example, if f(x) = sin(x)/x^2e^x, then f'(x) = (x^2e^x(cos(x))-2sin(x)e^x-x^2e^x(sin(x)))/x^4.

4. Why is the derivative of sin(x)/x^2e^x important?

The derivative of sin(x)/x^2e^x is important because it allows us to calculate the rate of change of a function at a specific point and also helps in determining the slope of a curve at any given point.

5. Can the derivative of sin(x)/x^2e^x be used to solve real-world problems?

Yes, the derivative of sin(x)/x^2e^x can be used in various real-world problems such as calculating the velocity of an object, finding the maximum or minimum values of a function, and predicting future values in economics and finance.

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