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Math Help - Differentiation

  1. #1
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    Differentiation

    Given that y = (1 +2x) ^ x , prove that dy/dx = y (ln (2x +1) +1 - (1/ (1+2x)) )

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  2. #2
    Super Member flyingsquirrel's Avatar
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    Hello !
    Quote Originally Posted by Tangera View Post
    Given that y = (1 +2x) ^ x , prove that dy/dx = y (ln (2x +1) +1 - (1/ (1+2x)) )
    y=(1+2x)^x=\exp\left[ x\ln(1+2x) \right]. Let u(x)=x\ln(1+2x). y can now be written y=\exp(u(x)) and the chain rule states that \frac{\mathrm{d}y}{\mathrm{d}x}=u'(x)\exp(u(x)) : once you have computed u', you are done. Does it help ?
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  3. #3
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    Hello!

    Yes, it helps a lot! Thank you for guiding me!
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