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Math Help - Differentiate x^(t-1) wrt t

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    Differentiate x^(t-1) wrt t

    How can we find the partial derivative of x^{t-1} with respect to t? This looks as if it should be really easy, but I'm not seeing it...
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    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by Amanda1990 View Post
    How can we find the partial derivative of x^{t-1} with respect to t? This looks as if it should be really easy, but I'm not seeing it...
    Treat x as a constant (let's say a). Then it is similar to differentiating \frac{\,d}{\,du}\left[a^u\right].

    So it follows that \frac{\partial}{\partial t}\left[x^{f\!\left(t\right)}\right]=x^{f\!\left(t\right)}\ln x\cdot\frac{\,df}{\,dt}.

    Can you take it from here?
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  3. #3
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    Quote Originally Posted by Amanda1990 View Post
    How can we find the partial derivative of x^{t-1} with respect to t? This looks as if it should be really easy, but I'm not seeing it...
    The easiest way is to let

    z = x^{t-1} take the natural log \ln z = (t-1)\ln x then take the derivative

    Edit. A little late
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