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Calculate the derivative of (x^2-5)^4 - (x^2-5)^3

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svjr | Student, Undergraduate | Honors

Posted November 12, 2011 at 8:43 PM via web

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Calculate the derivative of (x^2-5)^4 - (x^2-5)^3

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted November 12, 2011 at 8:54 PM (Answer #1)

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We have to find the derivative of: (x^2-5)^4 - (x^2-5)^3

y = (x^2-5)^4 - (x^2-5)^3

use the chain rule to find the derivative

y' = [(x^2-5)^4 - (x^2-5)^3]'

=> [(x^2-5)^4]' - [(x^2-5)^3]'

=> 4(x^2 - 5)^3*2x - 3(x^2 - 5)^2*2x

=> 8x(x^2 - 5)^3 - 6x(x^2 - 5)^2

The required derivative is: 8x(x^2 - 5)^3 - 6x(x^2 - 5)^2

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schwarzhand | eNotes Newbie

Posted November 13, 2011 at 1:17 AM (Answer #2)

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y' = [(x^2-5)^4 - (x^2-5)^3]'

=> [(x^2-5)^4]' - [(x^2-5)^3]'

=> 4(x^2 - 5)^3*2x - 3(x^2 - 5)^2*2x

=> 8x(x^2 - 5)^3 - 6x(x^2 - 5)^2

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