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# Product rule

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1. Am I using the product rule correct to work this out?
dy/dx = 4x^2e^(-5x)
so its 8xe^(-5x)+4x^2-5e^(-5x)
so 8xe^(-5x)-20x^2e^(-5x)
Im not sure if I simplified it correctly. Also am I right in thinking the product rule and the formula you use for integration by parts are different?

For some reason I am unable to post in the math study help section.
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Just quoting in Puddles the Monkey so she can move the thread if needed
Spoiler:
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(Original post by Puddles the Monkey)
x
3. (Original post by dont)
Am I using the product rule correct to work this out?
dy/dx = 4x^2e^(-5x)
so its 8xe^(-5x)+4x^2-5e^(-5x)
so 8xe^(-5x)-20x^2e^(-5x)
Im not sure if I simplified it correctly. Also am I right in thinking the product rule and the formula you use for integration by parts are different?

For some reason I am unable to post in the math study help section.
Yeah, different formulae, so dy/dx = u(dv/dx) + v(du/dx) with the product rule

d/dx(4x2e-5x) = 4x2(-5e-5x) + e-5x(8x) = 8xe-5x - 20x2e-5x
4. (Original post by dont)
Am I using the product rule correct to work this out?
Yes.

dy/dx = 4x^2e^(-5x)
so its 8xe^(-5x)+4x^2-5e^(-5x)
so 8xe^(-5x)-20x^2e^(-5x)

Im not sure if I simplified it correctly.
To simplify it further, pull out the exponential as a common factor:

Also am I right in thinking the product rule and the formula you use for integration by parts are different?
Well, you derive IBP from the product rule, so meh. I wouldn't really call them different, you're just rearranging an equation.

(Original post by Alexion)
Yeah, different formulae, so dy/dx = u(dv/dx) + v(du/dx) with the product rule

d/dx(4x2e-5x) = 4x2(-5e-5x) + e-5x(2x) = 2xe-5x - 20x2e-5x
Might wanna check that.
5. (Original post by Zacken)
Might wanna check that.
rip

this is why I'm gonna miss my grades
6. (Original post by Alexion)
rip

this is why I'm gonna miss my grades
You'll be more than fine.

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