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Math Help - Derivatives problems

  1. #1
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    Derivatives problems

    Find an equation of the tangent line to the curve at the point (1, 1).

    y = ln (xe^x^4)

    in order to find the slope i take the derivative so i use product and chain rule, it become (1/xe^x^4)(1(ex)^4+4x(ex )^3(ex)) and i know once i get the slope i can just use y-y1=m(x-x1) but somehow the slope is not right? is it the step i take the derivative wrong?
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  2. #2
    o_O
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    I'm assuming this is it : y = \ln \left(xe^{x^4}\right)

    If it is so, then you should be careful with your exponents. e^{x^4} \neq \left(e^x\right)^4

    So when differentiating e^{x^4}, it should be: e^{x^4} \cdot \left(x^4\right)' = e^{x^4} \cdot 4x^3

    __________________

    As an alternative, you can make your life easier by using some logarithmic properties first before differentiating:
    y = \ln \left(xe^{x^4}\right) = \ln x + \ln e^{x^4} = \ln x + x^4
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