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Math Help - Derivative of x raised to a function

  1. #1
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    Derivative of x raised to a function

    Differentiate:

    y=x^ {2-X}
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  2. #2
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    Quote Originally Posted by ahhh View Post
    Differentiate:

    y=x^ {2-X}
    Here's a start (assuming you're familiar with implicit differentiation):

    y = x^{2 - x} \Rightarrow \ln y = (2 - x) \ln (x) \Rightarrow \frac{1}{y} \frac{dy}{dx} = - \ln (x) + \frac{2-x}{x}.
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    y = x^{2 - x} \Rightarrow \ln y = (2 - x) \ln (x) \Rightarrow \frac{1}{y} \frac{dy}{dx} = - \ln (x) + \frac{2-x}{x}<br />

    Ohhhh...how can you tell when you need to use logarithmic differentation?

    I understand the process now. Thanks!!


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  4. #4
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    Quote Originally Posted by ahhh View Post
    y = x^{2 - x} \Rightarrow \ln y = (2 - x) \ln (x) \Rightarrow \frac{1}{y} \frac{dy}{dx} = - \ln (x) + \frac{2-x}{x} <br />

    Ohhhh...how can you tell when you need to use logarithmic differentation?

    I understand the process now. Thanks!!


    y = f(x)^{g(x)} is always a typical candidate.
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