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Math Help - Derivitive with the power rule

  1. #1
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    Derivitive with the power rule

    Can any one help me solve d/dx  e^(3x^2+8x)

    my answer of  e^(3x^2+8x)(6x+8)(3x^2+8x)+e^(3x^2+8x)(6x+8)  is not correct.
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  2. #2
    Moo
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    Hello,
    Quote Originally Posted by skyslimit View Post
    Can any one help me solve d/dx  e^(3x^2+8x)

    my answer of  e^(3x^2+8x)(6x+8)(3x^2+8x)+e^(3x^2+8x)(6x+8)  is not correct.
    Let u(x)=3x^2+8x

    So you have to find the derivative of e^{u(x)}

    Chain rule says : \Bigg([f(g(x))]'=g'(x)f'(g(x)). Here, g(x)=u(x) and f(t)=e^t \Bigg) -additional part-

    Hence we have that the derivative of e^{u(x)} is u'(x)e^{u(x)}


    Substitute u(x) and u'(x)
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  3. #3
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    Thanks, thatd worked. Now For more complicated ones (x-3)^9e^x

    I get  (x-3)^8[9(e^x)+(x-3)(e^x)] , but that is still not correct. Any suggestions?
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  4. #4
    Moo
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    Quote Originally Posted by skyslimit View Post
    Thanks, thatd worked. Now For more complicated ones (x-3)^9e^x

    I get  (x-3)^8[9(e^x)+(x-3)(e^x)] , but that is still not correct. Any suggestions?
    Hmmm well this is correct o.O
    But the completely factorised form is :

    (x-3)^8 e^x [9+(x-3)]=(x-3)^8 e^x [x+6]
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  5. #5
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    Thanks again )
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