swissgirl
What is the fourth derivative of \(f(x)=3xe^xe^{2x}\) ?



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bahrom7893
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well f'(x*e^x) = x*e^x + e^x = e^x(x+1). So:
f'(x) = 3e^x(x+1)  2e^(2x)
f''(x) = (3xe^x+3e^x  2e^(2x))' = 3e^x(x+1)+3e^x  4e^(2x)

bahrom7893
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f'''(x) = (3xe^x + 3e^x + 3e^x  4e^(2x))' = (3xe^x + 6e^x  4e^(2x))'
= 3e^x(x+1) + 6e^x  8e^(2x)

bahrom7893
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I think I made a mistake in f''(x)

Hero
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Yes, you did

bahrom7893
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No i didn't

Hero
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You made a mistake somewhere

bahrom7893
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f''''(x) = (3xe^x+3e^x+6e^x8e^(2x))' = (3xe^x + 9e^x  8e^(2x))'
= 3e^x(x+1)+9e^x  16e^(2x) <Final answer

swissgirl
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Btw u didnt go wrong

swissgirl
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Thankkksss Bahhhrrrooommmmmmm

bahrom7893
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Hero.. like i said.. ignore me.

Hero
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Yeah, that's the correct answer

Hero
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Why do you want me to ignore you @bahrom7893